Kind of, We WOKE up so early, you have to use the past tense. and "we could've been sleeping more" sounds a bit awkward, you might want to use "we could have slept more" instead.

"We woke up so early..." "We got up so early..." Both good beginnings, but use the past tense. "we could have been sleeping more" sounds unnatural/an awkward way to phrase it. Although adding "but" does make it slightly sound better.... I don't know it's kind of iffy. The following is better : "We woke up so early, but we could have slept (in) more/later." "We got up so early, but we could have slept (in) more/later."