ANYTHING is possible ...... There was a story (on here, I believe) about a guy in a very depressed and war torn part of Africa, who taught himself to read music, play the violin, conduct and compose symphonies. On his own, he gathered together other people around him, whom he taught to play various classical instruments. and started a symphony. They are now playing together, all of them having been taught by the guy who taught himself, and are gaining a good reputation.
Yes, it's clearly possible to teach yourself trumpet to a very high level, but it's going to be a harder road. Anyone who says it can't be done is simply wrong. It has been done, by a few of the famous players we talk about in here.
Even if you don't have a teacher, you probably aren't in a vacuum, and can get "instruction" on the fly from other musicians. This is how untold millions of guitar players learned how to play (most of the famous ones as well). No teachers, period. But, lots and lots of association with other musicians, who pass along chords, progressions, songs, etc.