Your chronology is right. Castro, while obviously very left leaning, didn’t announce his ties to the USSR until AFTER he had deposed Batista. Does anyone recall Castro being feted in the USA, and hanging out at the Hotel Theresa in Harlem, NYC ?
Most, if not all, of the idealistic young Americans who went to Cuba to fight with Castro in the mountains and on into Havana left his movement with that announcement.
Yes, I may be dating myself, but I was a youngster at the time I saw Edward R. Murrow interviewing Castro on CBS and praising him as "the George Washington of Cuba."
Yes, I recall the trip to the US, don’t recall where it was to though. Some people just cannot fathom that sometimes revolutions spark from within a country, not from outside of it. Check the US Revolution if you don’t believe that it can and has happened.
Me sense is, if Castro had been armed in any meaningful fashion by the commies prior to 59, the US would have stepped in to stop it.