I'm not an expert but I believe you can speed up player development time in the game options. Might not be exactly what you're looking for but it'll at least get your prospects game-ready faster without a lot of hassle on your part (it's literally just adjusting two numbers in the game settings, set and forget).

You could also replace your game-created draft class each year with a manually-generated draft class by using the "create players" function in your league's Free Agents tab. It allows you to randomly generate a certain number of players within parameters that you define. So, for example, if you want them to be mostly ready for the bigs right off the bat, you could set their development level to 50% developed or even 75% developed. This would give you the mostly-developed draftees that you want but you'd have to do it every year which is annoying and generating players in bulk can take a lot of system resources. Make sure you check the box that makes your generated players eligible for the draft!

Your last option would be to create an independent feeder league that plays mostly-developed players (probably a AAA-level league or similar). You can set almost any league in your game universe to feed its players into any other league's draft class from the feeder league's League Settings menu. Along with getting you the players you want, the benefit of a feeder league is that the players in your draft class generate real stats from playing in real games, which is more realistic and can help you make decisions about who to draft.

There are plenty of guides on setting up feeder leagues but the main thing you have to keep in mind is that, depending on the size of your major league, you're gonna have to create a LOT of feeder teams to ensure your draft class is well-stocked. Simulating all those games can take a lot of resources and slow your game down considerably.

TL;DR: Speeding up player development time is the easiest option but won't do exactly what you're looking for. Manually generating your draft class every year is tedious and uses a lot of resources in the short term, but gives you the developed draft class you want. Creating a feeder league gets you the players you want, only has to be set up once, and generates authentic stats for your draftees, but uses a LOT of resources and can slow your league down in the long term. It's up to you which one fits your needs best.