I remember watching an anime TV series in which the first episode had a young girl come across a dude slaying a dragon. He then took its heart to power a mechanized suit that he used to fight an invisible mech with the young girl's help who used cards to predict the future.

What is the TV show's name? I can't recall.

Maybe,.
The Vision of Escaflowne

Yes! Many thanks, stray! I'm going to watch this all day now.