No such thing as a "break in" as far as I know, but you should let the booster soak for at least a few hours before gluing. The recommendation by Haifu is 12-24 hours at NTP (So probably 20c and 1atm) but I've glued before that and it doesn't seem to influence it that much. It'll be soaked in by 4-5 hours. I could never measure any stiffness difference after 12-24 compared to 4-5, but the diameter may be different ie: tension different.
If you don't have a bat press, or if you wanna be more sure, then you should wait that 24 hours anyway before gluing just so the edges don't peel. You might need to wait closer to 72-96 hours if you go crazy with it and put on 3 thick layers. You probably don't need 3 thick layers if it's your first H3 sheet and you're using a soft sponge like 39A.
The edges will still peel when so boosted even if you use a bat press, but it should survive one tournament. Use a lot of glue. 3-5 layers on sponge and 2-3 on blade depending on the viscosity. Of course the sponge thickness has to be conservative to actually pass racket control, but I suspect they don't do it at your tournament.
You didn't say exactly how much you boosted and what the resulting hardness was so it's hard to say if boosting more will ruin it or not, but generally I wouldn't go under -5 hardness if possible.
Yellow will soften the sponge quite a lot, so you need to be a bit careful, although bear in mind that just taking the rubber off the blade will revert most of its hardness hence why you wanna measure it to know what you're dealing with.
I'm sure it's fine to put on 1 layer if you feel like it, and glue it with 3 on the sponge and 1 on the blade. Leave it in a bat press over night and it won't peel much at all. Play with it immediately next day for the best effect although it can be risky if you're not actually used to how freshly boosted and glued rubbers play.