Baker Mayfield's high school football coach, Hank Carter, tells TMZ Sports he couldn't be more proud of his former QB ... and tells Cleveland to strap in, it's gonna be one helluva ride!!!

Baker played for Hank at Lake Travis High School in Texas -- where the QB led the Cavaliers to the 4A state title in 2011. Dude racked up 6,255 yards and 67 TDs during his HS career.

So, we had to ask Coach Carter how he felt about Baker's insane NFL debut -- and guess what, HE WAS FIRED UP!!!

"It's fantastic! I'm so proud of that guy!"

Coach Carter says Baker's been loaded with potential for years -- and he's "not surprised" the guy is having success at the top level.

In fact, Carter says there's one thing Browns fans need to keep in mind -- this is just the beginning!

"No one will outwork that dude. That's the thing [the fans] gotta understand. He will not be satisfied with the success they had last night."

Congrats!