I know of at least one place where ita possible to go from zero to bachelor degreed paramedic.
UNM in AlbuquerqueOP, it's definitely possible - might not be advisable, to hear some folks tell it. It certainly seems plausible that there is benefit to having EMT-level experience...
Pitt?
Here in MA there are colleges that have both associate degrees and bachelor's degrees in paramedicine. You can attend them out of High School. I would recommend working throughout the program as a Basic.
Where?
Northern Essex Community College has an Associates and Anna Maria has the Paramedic Science Bachelors degree.