I have seen one form of using avoir, recently, like this: à avoir eu. I forgot the phrase itself, but, for example in this phrase I just found in Google: Les jeunes de l’OM sont 2 sur 14 à avoir ...
When learning French, I was taught that an infinitive form, e.g. jouer, meant “to play” (or whatever). That is, the English translation of the verb was preceded by to. The word à also means “to.” But ...