Consider not applying for product management roles. Most PMs get into tech product management after they’ve done some other job in a tech company, like software development, QA, marketing, support, etc.
This is not an accident. Most candidates really benefit from having more diverse career experience, because PM tends to be generalist role where you need to know a little bit about everything, so getting a wider vantage point is helpful before jumping in to a PM job.
Also, PM tends to be a role where seniority (being more experienced than your colleagues) really helps because the role has little formal authority so you can only get your colleagues to do what you want if they have a lot of respect for you and your opinions. If you’re a PM whom your colleagues don’t respect, then at best you’ll end up doing menial tasks for your more-senior colleagues and at worst you can’t get anything done and they’ll work around you instead of with you. No fun in that!
If you’ve already done a PM internship or have PM experience and have received strong positive feedback from your manager and the team of cross-functional colleagues that you worked with, then you can disregard my advice above because you already have the experience necessary.
Or you might be a PM savant who was hatched knowing how to design products, manage products, work with super-smart engineers, understand and communicate business priorities, with top-notch UX sense and calm under pressure. If so, apply away.
But if not, I’d definitely consider a more circuitous path to product management, because you’l be following the most commonly successful path that others have tried before you.
Full disclosure: I worked as a software developer for several years before switching to PM. So I’m biased. But most of the PMs I’ve worked with also didn’t start as PMs, so AFAIK this is objectively the most common way to do it.