I can't pin it down definitively for you, but I can narrow down the field for you to 'no later than 1991'. Let's use the term 'Take 10' for what you're looking for, and have a closer look at some systems through the years, and see if we can find a time when it came into being.
I suspect that a dice pool mechanic was more likely to generate the idea of a 'trade-in roll for basic success' rule, and dice pool mechanics were not in common use until at least the late 80s. The d20 system is one notable exception to being a dice pool system with a Take 10 option, but in the case of d20, they fix the roll and not the result, unlike other examples. For this to work, there needs to be some meaning to 'you only just barely succeed', meaning you need opposed rolls of some sort, or degree of success.
The original Traveller system, which is the earliest skill-based system I have access to, written in 1977, features only a very rudimentary skill system. Certain rolls with high enough modifiers cannot fail, but there is no option to trade the roll for a minimal success. There are no degrees of success either.
Robotech RPG (1986, based on Palladium system) has no Take 10 - skills have to roll under a skill value, which can't go higher than 98%. Since the target number is always fixed, and there is only binary success, there is no meaningful way to add a 'Take 10' type of rule. I suspect the same would apply to any other 'roll-under-skill' system, such as Chaosium/Call of Cthulhu, 1e Twilight:2000 and Rolemaster.
Megatraveller, from 1987, also does not feature explicit, automatic success. Some tasks cannot fail, simply by virtue of the modifiers involved, but in theory, you still have to roll. MT has degrees of success, but still no 'Take 10' option (or would that be Take 7?)
The earliest version of Gurps I have access to (3rd ed, second printing, from 1989) mentions automatic success, but this is totally GM fiat. So long as the GM believes there is any chance of failure, a roll must be made, and a certain value on any roll is automatic failure. Again, I can find no mechanic for trading out a roll for a fixed result, and I see no reason why the rule would appear in earlier versions, but not later.
First ed Shadowrun, from 1989, has no concept of automatic successes, even though it does have degrees of success, and a dice pool mechanic.
Vampire the Masquerade 1st edition (1991) does feature automatic success, on p36.