When to transplant seedlings?

Good morning folks!

I have acclimated about 10 of my seedling trays and all have survived the introduction, my question is when can I transplant them?
The seed was planted in take away containers with glad wrap covering and now that they are uncovered they dry out rather quickly, watering is difficult because there are no drainage holes and I have to be careful I don't drown them, it would be much easier to manage if they were in proper pots. The seedlings are small and I am worried moving them will kill them.
Should I just continue to persevere until they are a bit bigger?
The oldest are about 7 months.

I sow seeds in spring and 1st transplanting is next spring when seedlings are 1 year old.
It is possible to transplant 7 months old seedlings but seedling size of each species is different.
It depends upon the size of seedlings.

I keep seedlings in wet and semi-shade condition for 2 years in total including after 1st transplanting.