As it's not SOP to have one guy working both tower and ground at an airport the size of LGA, I'm going to assert that the most likely scenario is that, yes, there was no way to even have a relief available.

What caused the lack of availability is the well-documented understaffing. Everyone in aviation knows that ATC is understaffed right now, and the reasons for the understaffing are well-understood. To come in and instead say, "well, I'm a mathematician, I'm going to make some simplifying assumptions - the only simplifying assumptions permitted - and do some basic arithmetic to show that there were hundreds of controllers available, clearly the guys responsible for ATC at LaGuardia don't know as much about running an airport safely as me" is beyond silly.