I can't for the life of my wrap my head around how in a mere hundred years, Christianity went from being the victim of attempted eradication, to the state religion that got in to the business of the eradication of its enemies itself, both outside (paganism) and inside (Arinaism. Well, kind of, but you get the point.)
Personally, I believe that people in history have no agency. Society has laws (I do not mean the legislative ones, but more like that of physics) and people are just swept in the currents. When "we" change something, that's society reshaping itself according to its own laws, we are just cogs in the machine, like how a clock jumping a minute is not a decision of its cogs, but a result of them functioning in a system. This is why it feels so... strange to think that Constantine single handedly set original European culture on to a course of extinction (and to be the victim of cultural cannibalism, looking at you saturnalia Khm I mean Christmas.)
So, Constantine legalized christianity and empowered it because he needed political support, that much is clear, which fits in to the "No Agency" thing. He didn't do it out of conviction or belief: Society's laws dictated he has to, in order to stay in power. Was there ever another option? If the other guy won the bid for the Imperial throne, could he have had the option to do anything else if he wanted to stay in power?
FAQ; fantastic responses on the general how/why here and specifically on the impact of Constantine’s conversion here both by u/talondearg.
There’s also “the rise of Christianity” by Rodney stark, although it’s a bit dated and disputed now. Pretty sure talon would have an opinion on it; and the topic is always open for more and different discussion tho.
Apart from the prior thread linked to by /u/avid_snotbody
'No Agency' is really a philosophical presupposition you seem to be bringing to the table, and I wonder why 'society' has to obey laws as in some kind of deterministic universe. That is ultimately a particular view of the nature of reality, humanity, and history. And it's mostly beside the point of your question. Though I do think it skews any attempt at history you're going to do - because you think what any individual actor does is either negligible or pre-determined.
But it also means you have to explain all 'great man' moments the same way. Our old friend Chinggis Khaan changed the course of history across Asia and Europe in his lifetime in ways that aren't not explicable without him. I suppose you could abstract and say, "If not Chinggis, then deterministic forces would have created someone exactly like Chinggis and the exact same outcomes would result".
But Chinggis is a great counter-example because the pace of historical change does not have to be glacial, it can be rapid. When Constantine took over, it's very debatable that he needed the political support of Christians. Most demographic estimates put Christians at about 10% of the population then. He doesn't need Christians, so it's not clear at all that he did it out of political support. Also, whether he did or not does not tell you whether he also did or did not act out of conviction. Political advantage does not disqualify genuine belief.
Could Constantine not have 'backed' Christianity? We'll never know. There's no way to run 'speculative history' control experiments. But the immediate circumstances of his 'conversion' certainly do not support the narrative that he had to convert, or that if he'd lost the civil wars, his rivals (say, Maxentius or Licinius even) would have had to convert.