It doesn't sound right. Seems like by this time you should see some real growth. Where did you get the seeds?

That looks nothing like a begonia seedling. I agree it looks like algae, moss, or something similar. You did surface sow? No covering of the tiny seeds whatsoever?

Here are a few pictures of my own seedlings (easy to germinate but you need the patience of Job to prick them out and move them to their first pot).

This was begonia and coleus seedlings in a pie plate with clear lid.

some seedlings (how many weeks I don't know) and a cobra fern

Sometimes I just open a capsule and sow it on a pot of other begonias just to see how fast they germinate - most will never make it with this shotgun approach though.

Yep, with such a fine seed, I know not to cover. Ok, umm I guess I'll see what species of liverwort or fern I'm cultivating by fall. Begonias just aren't my thing..I'm finally getting rexes to do decently (not great), and my b. dregei hasn't exactly died (though not flourishing). I do well with most thing..but begonias (argh). Maybe next year, I'll order B. sutherlandii plants.

Keep plugging away. If I can do it, anyone can. It does take a lot of patience and practice and I still lose many over the course of a year.