You can do it with more conventional methods or you can use trade cheats to get it done. Such as using the SAR. If you do not know what that is, it is a trading method where you get a team to release a high overall player like RE Aaron Donald. The SAR is trading lets say the Rams 3 REs from the Free Agency during the regular season for a late-round draft pick. This will get Aaron Donald released to you.
The goal is to do this with high overall players that teams will show high interest with to trade away their 1st round picks. Do the SAR with two good REs like Aaron Donald and Myles Garrett. Both will more than likely show high interest and will get you any 1st round pick if you try and trade them to a team. After you get that teams pick, do the SAR again by trading them 3 more free agency REs to get Donald and Garrett released. Continue this process until you have reached the max amount of draft picks.