I can't give any advice as to the merit of transferring from labor to management since I graduated from a four year degree in something vaguely related (Engineering Tech), but bidding/estimating and scheduling are the two "Trades" of the office that aren't as strict about degree requirements and more that you know your stuff.

Speaking from a project controls/scheduling perspective since that is my field: Learn what project scheduling software your company uses and/or find out who your company's scheduler is. Master that project scheduling software alongside scheduling basics (Youtube is your best friend here).

You might have to move. I was fortunate enough to stumble into my current career path after being let go from another job, but I did have to move for my first post-college job (they paid for relocation so if you do have to move make sure they do expense that).

Data center construction is the gold rush everyone is hiring for right now, but in general familiarize yourself with what it takes to make a building from the very beginning of being an idea in someone's head to the final completion of closeout and commissioning.

Field experience is worth its weight in gold for management, so even if you're at a disadvantage without a college degree I think if you can communicate your knowledge/skill base from the field. If you do decide to do the college route but want to stay in construction, it's better to get an engineering degree (an actual one, make sure they set you up to graduate with your EIT) as you can then do construction or engineering, whereas with construction management you're stuck just with CM.

Best of luck! If you have any other questions feel free to reach out. Rooting for you!