The first reason is that God judged it the right time.
From a human socio-political framework, the Roman Empire was the first empire to establish a real parliament, it had well defined laws, a system of engineering and roads far ahead of any other previous empire, which meant missionaries could travel relatively easily. It endured for a thousand years from rise to fall (that’s five times our Australian history in the European sense and nearly four times US history). It had religious freedom with the exception of compulsory homage to the emperor.
Peter and Paul did not go to Rome for no reason. Paul was able to appeal to cast iron laws, as a Roman citizen, to go to Rome to appeal to the Emperor himself. He couldn’t have done that under the Assyrians, Babylonians, Persians, or Alexander. Likewise Paul wasn’t chosen by accident either. His personal Roman citizenship was an integral part of his ministry.
There was peace of a sort which allowed Christianity to spread within its empire. There were Jews all over the place, not only due to trade but previous dispersions, thus providing a reference point for the new religion.
There was a lingua fraca, the Greek language, due as much to Alexander as anything else.
There was a high level of philosophical and moral thought in Greek and Roman literature.
It was well administered. Some women had influence in high places. It was not a tribal society, as some Middle Eastern nations are even today.
In short, the Roman Empire and the political world of the time suited the spread of Christianity as no other empire had up to that time.
We might argue that God can do anything, which is true. But in practice He usually delegates as much as possible. If He was to delegate the job of spreading Christianity to humans (and He only spent 3 years in direct human ministry Himself before handing the responsibility over), then He would have to do so when conditions would allow them to spread the message with some sort of realistic timetable.
WIth hindsight, the Roman Empire was possibly the first time that it was feasible, given human constraints.