First, plug the hole with a towel or something. Now, me I'd take the tank off first (unless a one piece toilet). Turn water off, flush, remove tank lid an use a sponge to remove water left in tank. Disconnect the water line. Use a screwdriver to undo the two (three on some models) brass bolts. Put towels down on the floor or tub. Lift tank an place on towels. Now, see if you can get the snake.
If no. Remove water from bowl an put a towel in it. Lift the plastic caps up on the base of the toilet so you can see the nut. Loosen both side a little bit first. Then undo them an remove the nut from the stem. Now, before you lift the base you're gonna want old towels an or cardboard. Why? The base has a nasty, sticky wax seal an you don't want that on anything. I would put some cardboard next to the base an rock the toilet forward sliding the cardboard over the 4"pipe. 10 to 1 the snake is in a camber you still can get too.
Before you do anything you might want to go to Lowes, Home Depo or your local store. You'll need a new wax ring an toilet base bolts(stems). Might as well get the rebuild kit with the new washers, bolts, gasket like this:
https://www.walmart.com/ip/Fluidmast...87d2f612ac6bca
If your snake is in a chamber that can't be reached. Lock the base up an wait.
Good luck! If your near OC, Md I have tools.