Yes, quite easily.
I’ve used the technologies and manufacturing techniques available in the Bronze Age to produce a hand-launched model to see if it would glide, it did, very well. Its sink rate is better than a modern delta hang-glider. I’ve built experimental aircraft for the Ministry of Defence and was curious if a basic glider could have been made with those manufacturing technologies and materials they had to hand and were proficient using.
The answer is yes they could have, one also needs to consider the account, I don’t think a hand-launched model would warrant this story being kept alive in the oral tradition, a demonstration from a tower a possibility, a successful long-distance flight (at least for Daedulus) viable if Island hopping is used to obtain approximately 2kms of altitude to glide up to 50kms to the next island (assuming no headwind). The instrumentation needed is no more than a scarf on each handrail, if the target island is below it, you have sufficient altitude for the passage.
We should not underestimate how sophisticated and good the Minoan understanding of hydrodynamics was (it's not modern but it is very good), hot (heated) and cold running water is present in the Queen's bathroom at Knossos palace, (venturi) injectors are used in interlocking claypipes to remove debris, the white ship hulls are hydrodynamic to slip through water with minimal resistance (one appears to use copper filings rather than limestone powder, to repel shellfish attaching to the hull), there is a lot of evidence that the Minoans built theoretical models (of the celestial bodies) and physical model of ships and buildings before attempting to scale up. They were very good and talented practical engineers and did undertake things in a methodical and surprisingly scientific way (magnetic declination is recorded in building orientation to Magnetic North from around 1800 BCE for example).
One can debate if the fabled account of Icarus and Daedulus is true or what was actually demonstrated, we may never know.
The Greek text although obviously lacks modern terms are hugely interesting to an aero engineer, the following is described:
a) a cambered (lift-generating) wing,
b) a tapered wing from the centreline (in planform) towards the tips, the feathers are used to describe that the wing is not straight but elliptical on the trailing edge, a complex shape like a bird is described, very specifically, this is Griffon Vultures (indigenous to Crete).
c) constellations are unequivocally referring to angles to exclude a (flight) path from Orion (on the horizon) to the Great Bear (upwards), it is explaining a shallow glide path (slightly nose down), correct, Daedulus seems to understand that there is minimum glide angle!
d) weight is balanced below the wing.
This suggests an understanding of the principles of gliding flight. You would need to build at least a model to understand this. I’ve included the text at the bottom and highlighted the sections which will be of interest to aero engineers. If you read the description carefully, the feather are not used to describe apparatus but a shape in plan (form), a Griffon Vulture’s wing!
The Minoans had technical skill in building very lightweight composite structures. Specifically, shields, which used a wooden frame, a wicker core to absorb impacts (balloon baskets still use this method as the material can withstand hard impacts on landing), and layers of leather bonded and stitched.
We actually don’t know very much about the Ancient usage of natural resins beyond incense and it is likely that there were other more technical applications, we know there was a trade in resins as they are found in shipwrecks, we don’t really know what they were used for (but large quantities and a variety of different types are present).
A team that reproduced this Theran half-scale Minoan white-hull ship shown below, used flax linen cloth over a wooden frame, with resin (a natural thermoplastic), fat (which I presume acts like a plasticizer, tree resins can be brittle) and limestone powders to make the white hull ship watertight, this has many advantages: hydrodynamic, completely sealing the hull and is used inside and out according to the fresco (if the ship is caught on rocks, the inner layer would delaminate but likely keep the hull watertight until landfall where a repair can be made). Ancient people (or at least the Minoans) may have been able to create complex composite structures using natural materials (possibly lost in the Bronze Age collapse, the ship Theseus returned in was kept in Athens as a prize for centuries until it decayed, no other civilisation could even reproduce these hulls, it is only the Minoans that use them or know how to make them! Flax is almost as strong in tension as glass fibre and very abrasion-resistant. The Minoans were brilliant at making things including textiles. They produced the finest weaves at this time, not just flax but sea-silk of gossamer fineness.
The first aircraft used linen (called aerolinen) over a wooden frame and sealed using resin. The Minoans had all these very same materials and the very best craftspeople. I also note Icarus is accredited with inventing the sail. I don’t think its the sail, this was known well before this, I think it more likely a seal to improve the longevity of the sail at sea or possible nets which are used to transfer loads to the mast under wind loading!
This is a casting in Bronze from Samos, ca, 700 BCE (so likely a millennia after the mythical account). I used it as a model to create a wicker frame elliptical top wing (but elected to use a top fixed wing rather than the mid-wing shown), the wicker frame skinned with linen cloth and sealed, the pilot held using a leather harness but able to move about using the two wicker handrails (as shown). I used a wooden mannequin for weight shift and the legs are splade (using linen inbetween), the glider benefits from extended the control surfaces backwards with poles that could have been inserted into a sleeve in flight from the knee down, however, glides without (with less stability in flight). It is a simple elegant airframe, wingspan circa 6–7m. I should also add, competition hang gliders use this configuration as its technical better.
The Minoans had all the same technologies the early flight pioneers such as Cayley had and arguably better craftspeople that were very proficient with using these manufacturing techniques and materials if we assume Daedulus is the master crafts person to Minos, then he has access to the Palace workshops which can make practically anything. They also have an advantage over the early tower jumpers, they had not heard the tale of their exploits which suggest feather were used! Which would be unlikely as they were proficient in creating sails. They more likely modelled the shapes and planforms on a Griffon Vulture which can be observed rising on the sunny side of a hill (using thermals), present on Crete.
Daedalus plans his escape from King Minos of Crete
Meanwhile Daedalus, hating Crete, and his long exile, and filled with a desire to stand on his native soil, was imprisoned by the waves. 'He may thwart our escape by land or sea' he said 'but the sky is surely open to us: we will go that way: Minos rules everything but he does not rule the heavens'.
So saying he applied his thought to new invention and altered the natural order of things. He laid down lines of feathers, beginning with the smallest, following the shorter with longer ones, so that you might think they had grown like that, on a slant. In that way, long ago, the rustic pan-pipes were graduated, with lengthening reeds. Then he fastened them together with thread at the middle, and bees'-wax at the base, and, when he had arranged them, he flexed each one into a gentle curve, so that they imitated real bird's wings.
His son, Icarus, stood next to him, and, not realising that he was handling things that would endanger him, caught laughingly at the down that blew in the passing breeze, and softened the yellow bees'-wax with his thumb, and, in his play, hindered his father's marvellous work.
When he had put the last touches to what he had begun, the artificer balanced his own body between the two wings and hovered in the moving air. He instructed the boy as well, saying 'Let me warn you, Icarus, to take the middle way, in case the moisture weighs down your wings, if you fly too low, or if you go too high, the sun scorches them. Travel between the extremes. And I order you not to aim towards Bootes, the Herdsman, or Helice, the Great Bear, or towards the drawn sword of Orion: take the course I show you!'
At the same time as he laid down the rules of flight, he fitted the newly created wings on the boy's shoulders [this is hugely important, it does not say attached flapping wings to the arms! It is a fixed wing and Icarus is holding its initial weight on the ground in his shoulders]. While he worked and issued his warnings the ageing man's cheeks were wet with tears: the father's hands trembled.
Icarus and Daedalus fly away from Crete
He gave a never to be repeated kiss to his son, and lifting upwards on his wings, flew ahead, anxious for his companion, like a bird, leading her fledglings out of a nest above, into the empty air. He urged the boy to follow, and showed him the dangerous art of flying, moving his own wings, and then looking back at his son. Some angler catching fish with a quivering rod, or a shepherd leaning on his crook, or a ploughman resting on the handles of his plough, saw them, perhaps, and stood there amazed, believing them to be gods able to travel the sky.
And now Samos, sacred to Juno, lay ahead to the left (Delos and Paros were behind them), Lebinthos, and Calymne, rich in honey, to the right, when the boy began to delight in his daring flight, and abandoning his guide, drawn by desire for the heavens, soared higher.
His nearness to the devouring sun softened the fragrant wax that held the wings: and the wax melted: he flailed with bare arms, but losing his oar-like wings, could not ride the air.
Even as his mouth was crying his father's name, it vanished into the dark blue sea, the Icarian Sea, called after him.
The unhappy father, now no longer a father, shouted 'Icarus, Icarus where are you? Which way should I be looking, to see you?'
'Icarus' he called again.
Then he caught sight of the feathers on the waves, and cursed his inventions.
He laid the body to rest, in a tomb, and the island was named Icaria after his buried child.