Sometimes the phone can surprisingly have a more powerful amp than a PC motherboard, if not better DAC. At least, this is quite common with Apple phones v Windows laptops.
While I can't vouch for DT 770 and Soundblaster G1, those were the headphones to go for if you needed noise isolation, and there's no real reason the G1 shouldn't work well with them if you end up needing a cheap amp solution. For something above 300 Ohms I'd probably get a better soundcard than that? Sensitivity comes into it as well though, not just impedance. It's actually hard to tell, on paper, what'll be a good match. And motherboard makers might exaggerate about onboard amplification as long as you can still hear "a whisper".
So if you're not entirely happy with the oomph or features of the motherboard audio for some reason, and try out the G1, take note of something Creative doesn't specify on the product page - you need to install both sets of software including the Xplus Configurator. On this Xplus thingy, you need to set the headphones to "Generic". This is because out of the box the soundcard is set up for PS4 with less oomph. Then you could use the main software to add Crystalizer (warmer, fun sound) if preferred, etc etc. Personally, I have some Crystalizer and some Bass enabled, with Surround, Smart Volume and Dialog Plus disabled. But this depends on the headphones and one's own taste.