Like @bob31 I use a spray bottle to water my sprouts, making sure
It's pH 6.5 is very important. A few spritzes a few times per day. The jiffy starter is very absorbent - I give a few spritz to the tops of the leaves then a few right on the soil surface. I also keep mine in this dome to hold in moisture, and I spray a paper towel and place it in the dome to add to the humidity . I bought it on Amazon for about $15, and I lay the T5 light right on top.
I think you will be good to transplant once your soil arrives - if you have five gallon pots to move them too you may as well - might be the best approach for these sprouts since they are a little stressed now - may be gentler in the long run for them.
Happy farming and welcome to ILGM!
Bt the way - are you in the USA?