Nope. For the longest time, the bulk of Ukraine was a part of Lithuania.

Polish-Lithuanian commonwealth

Eastern and southern parts of Ukraine were a part of various Turkish Khanates for the most part. Those lands did eventually become a part of Russia, but only in the 17th and 18th centuries. Russia finally conquered western parts of Ukraine only during the Second partition of Poland in 1793. Ukraine remained under Russian control until 1917, when Russian empire ceased to exist. They were ceded to Central powers to rule through proxy kings via the treaty of Brest-Litovsk.

Entente made Germany renounce the treaty and the newfound People’s Republic of Russia invaded the newly independent Ukraine, Belarus and Poland. They managed to conquer the first two, establish a Soviet government and proceeded to establish a completely new entitly, the Soviet Union. From the legal perspective the Soviet Union wasn’t a state, but a supranational entity like the EU is today. It had fifteen member states, thirteen of which conducted international relations through the Soviet Union and two had independent foreign policy - Belarus and Ukraine.

Ukraine was under Russian rule from 1793 to 1917, for a total of just over 120 years. The central and eastern parts were under Russian control for another 150 or so years. Ukraine was a part of a Russian state in some shape or form for about 300 years in total. They haven’t been a part of Russia for over 100 years now though and it’s pretty clear they don’t want to.

By way of comparison, Ukraine was a part of Lithuania for longer than 300 years. So no, Ukraine was not “always” a part of Russia. It was a subject of Moscow for a few centuries, but even that ended over a hundred years ago. There’s no historical claim to speak of here.