I am sure that some others will chime in...
but although there are general rules about when/how frequent they will lay there are many factors that go into it I will list a few that I know of.
First...you need the age. Some birds (birds not breeds) will start laying as early as 18-20 weeks. Others may be 30 weeks before the first egg.
Next, LIGHT. The amount of daylight they have each day affects the number of eggs they lay. This is a big one. Sometimes I even get less eggs on rainy days when the hens hang out in the coop most of the day.
Also, diet and metabolism. I feed layer mash and my birds free range. Again, if they hang out in the coop all day or I have them up in the run for a day or two production decreases.
Too, it takes then a while to start producing on a regular (everyday) basis. They may go a day or two in between when they first start. If I have a few low production days I feel of my birds bellies (underside) to make sure they do not have an egg that is stuck or anything. But it took my hens about a month to be consistent. For example, I have 12 laying hens in one area, for the first month I got about 5-6 eggs per day, then up to 9 per day, now I get 11 or 12 every day.
It just takes time.
You guys seem to be doing a wonderful job! Waiting is hard!!!