If you google around a bit and look at the state of U.S. commercial aviation in 1945, flying from New York to Los Angeles was a lot more difficult and arduous than the movie leads us to believe. In fact it appears transcontinental routes were not introduced until 1946. After promising Fontaine he would take care of his problems, Vito tells Tom to get on a plane tonight, and go to Hollywood and straighten things out with this Hollywood bigshot.
Likewise, on his return to New York, Tom says he "slept on the plane."

Considering that the wedding probably took place on a Saturday, and further considering that there had to be a meeting "next week" with Sollozzo, I have some real questions about how Tom could pull this off.

Even if you assume there was a plane leaving New York late that day, it would have taken Tom about 20 hours to fly coast to coast. There were no set intercontinental routes until 1946, which means Tom would have to take puddle jumpers stopping in more than half a dozen (at least) places between the two cities, and in all likelihood he would have had to change planes. The best case scenario then is that Tom would have arrived in LA on Sunday, checked into his hotel and manage to get an appointment with Woltz the following day. It would also mean that the dinner with Woltz took place that same day, which means Woltz was able to "check him out" and make dinner arrangements that same day. After Woltz does his rant, Tom asks if Wolts' car could please take him to the airport. This means that Tom had already checked out of his hotel and knew there was a flight back to New York on Monday night. Another 20 hour flight and
consideration for the 3 hour time change at best would put Tom in New York late Tuesday night when he tells Vito "I slept on the plane." If you watch the saga you know that they planned to send Luca out to kill the horse. Woltz finds the horse head in his bed in the morning, which means at best Luca would have flown out Tuesday night (again assuming there was a flight with tight connections) arrived Wednesday, and killed the horse Wednesday night, meaning that Woltz awoke on a Thursday. If this is to be believed, then the meeting with Sollozzo was on a Thursday because that same day Vito got the flowers from Johnny
thanking him for getting him the role. This would mean Woltz called Johnny who was in New York someplace resting and eating at Vito's request, and told him he had changed his mind.

Furthermore, it would mean that Luca got out of LA Wednesday after he killed the horse and got back to New York in time to have the meeting with Vito about going to find out what was underneath Sollozzo's fingernails.

I could not find anything specific about flight shcedules in those days, but it seems highly improbable one could just hop on a plane to LA (as one can do today) at any given hour of the day, let alone do a round trip and the Luca trip in such a short time period, in which case the timing of the Solozzo meeting is impossible, even if you assume it happened on a Friday.

Any aviation enthusiasts out there who can help out with this one?

And please no smart ass "Maybe the Corleones had a plane" comments!

P.S. Oddly, in GFII at the dawn of the time when people flew comercially on jets, Michael goes to Miami on a train!