For most two-move checkmate problems, the answer is yes. But a few, mostly human-designed two-move checkmate can be very difficult. There are a lot of such problems floating around, some may be hundreds of years old.
To design a one-move checkmate problem, there are normal 2 to 5 places that can be checked, at most 10 places which are rare. You just verify each check to confirm it's a mate or not.
For two-move checkmate problems, the designers had painfully taken care of all the variations. Normally the first move can have 5-10 choices, more when the first move is not checking the King, and there may be 5-10 possible defenses, and then for each defense you need to find the followup mate or confirm there is no mate in that variation. The paths that need to be checked may be ballooned to 10 x 10 = 100. It's not easy to find all these paths, and to remember all these paths (because you want to make sure that you have exhausted all possibilities), and to calculate all these paths.
Jumping from 5 simple checks to 100 checks is huge for our brains.