The question is simple, how many competitive matches do you need to unlock overwatch function in CSGO? Or what range do you need to be to unlock this function?
There is no set number of games or objectives to complete, to get Overwatch access. According to the wiki:
Investigators are selected based on their CS:GO activity (competitive wins, account age, hours played, Skill Group, low report count, etc.)
Basically the older your steam account is, and the higher your in-game rank, with high percent accurate reports, then you have a pretty good chance to get selected, as long as you haven't been correctly reported (say griefing or scripting)
Though my steam is not that old (don't even have the 5 year badge) and my rank was mid level when I got it, so I believe the most important thing is accurate in-game reports of actual cheaters (or griefers/scripters) you encounter.
It's technically not defined by Valve but many users have said they unlocked it around Master Guardian range and immediately when they hit 150 wins. I was Master Guardian and didn't have it unlocked, presumably because I had only like 70 wins or something. One friend had around 300 wins when it came out and didn't unlock it till about 350. So there really isn't a defined range, it's kinda random.