Moving nonverbal 23 month old with "suspected ASD" to toddler bed?

So, my son Dean is 23 months old and hasn't spoken his first word yet. He also doesn't seem to understand much of anything I say, "no" included. He was in speech therapy for six weeks, but the online format wasn't right for him and we are waiting until we can have in person visits to start him again. In that time, I mentioned my concerns that he may be on the spectrum. His therapist agreed and said she saw many red flags, but that he wasn't old enough to be referred to a specialist yet.

Anyway, Dean sleeps in a pack and play. He learned to climb out at 15 months, but it was so sporadic (once every couple of months) that it wasn't a problem. But for the past week, he has been climbing out of his bed 5-10 times a night. And considering the fact that he lands on his head, he has to be moved to a toddler bed.

But Dean hardly sleeps. I put him and his three year old brother (who sleeps in the same room) to bed between 8 and 9. But Dean won't fall asleep until midnight. Then he wakes around 3 for an entire hour. And wakes up at 6 in the morning. Sometimes he takes a nap for an hour in the middle of the day. Other times he doesn't nap at all.

For anyone who's had experience moving a suspected or diagnosed toddler with ASD to a toddler bed, how can I make the transition easier on him and me? And how can I do it without disturbing my sleeping 3 year old too much? I also have an 8 week old, who needs regular feedings at night. And my husband works nights and is therefore not here to help, so I have to do this on my own.

Any advice from someone who's been in a similar situation? I have his bed ordered and I'm just so stressed thinking about how hard this is going to be.