As most of the cavity nester were having cavity nest in the difficult to access places , so is there any method to know the exact dates with out looking inside the cavity.
Sir you need an endoscopy camera with attachments to your smart phone it will cost less than 10000 Rs, or you can use motion detractor Wifi camera with night vision facility for more precision
I agree with the above answers, and would just like to add some things that might help you predict hatching times. If you have limitations on how long you can record inside the nest, or how often you can visit the nest to check progress, the information could be helpful. (and I apologize if I am telling you something you already know!)
If the bird begins incubation immediately after laying the the first egg, then the eggs should hatch in the order in which they were laid. This would mean you need to observe the nest for several days from the time the first egg begins to hatch (at least as many days as number of eggs). If the species begins incubation only after egg laying is completed, then you should have relatively synchronized hatching and would only need to observe for 1-3 days until all chicks are hatched.
It would also be very helpful to know the incubation period. You could try contacting zoos or breeders who have successfully bred this species to find this information, if it is not already available in the literature. As there is so much variation in incubation time between species, knowing that information in advance could really save you time and effort.
If you don't have the incubation period or laying/incubation behavior for that species, you will probably have to regularly check the nests or your recordings to wait and see what happens.