No, that's not the rules.
The DM determines if a check is allowed, and if so, sets the DC for that check.
The GM calls for an ability check when a character or monster attempts an action (other than an attack) that has a chance of failure. When the outcome is uncertain, the dice determine the results.
Ability Checks - 5th Edition SRD
If an action has a chance of failure, or if the outcome of that action is not certain, then
the DM may call for an ability check to determine success or failure. Otherwise you automatically fail (or succeed) in the task at hand.
If a PC wants to jump to the Moon, or persuade the King to hand over the Kingdom, the outcome is certain (failure). As the outcome is all but certain, there is no check called for by the DM, and the PC just fails. If a PC wants to climb a ladder then there is no check required, there is no check called for by the DM, and the PC just does it.
Players dont call for an ability check. The DM does, and only when that players character has an appreciable chance of success in the task at hand.