Did you take the seed out of the covering? You need to remove the outer 'shell' to expose the seed, then plant it. If it has a tap root, it's already trying to shed the shell, so go ahead and pry it off. If you break the tap root, it will not grow.

Mine takes about 2 weeks before I seen a shoot. I think a little more time was needed. Digging to check for sprouting is a bad idea because you can easily damage sprouting roots without realizing.

Your impatience with digging it up prematurely probably has ruined your first seedling(but leave it in and see if it comes up). The mango seed will send out a tap root headed down first and then it sends up the sprout that breaks the surface. Here in Florida the quickest I've seen the sprout break surface is 8 days, but I've had others take a whole month. Best way is to plant the dang thing, leave it alone and let nature do her work. Make sure you open the hard shell carefully (like opening a clam) then plant the seed flat in good potting soil like Miracle Grow Potting Soil in a one gallon container to start. Keep the soil damp, not wet. In the Fl. hot weather here they usually sprout within 2 to 3 weeks.