For a gtx 770 you are better off with a 550w psu. For several reasons. It'll generally have the pcie connectors needed by the card. You can get away with using adapters from the molex, but that's really not recommended. The 550w will have plenty of amperage on the 12v rail. This is important because that's where the wattage comes into play. On a 450w, you'll be pushing the limits of what else is dependent on that 12v rails amperage, like the cpu, fans, Sata etc and one good spike can starve components, black screens or blue screens are common. The G4400 is such a low draw cpu though, that this shouldn't be an issue and there's no OC to complicate matters.
And then there's the psu itself. Psus are not created equally, they'll use different platforms and different components, even different quality of such. If that Evga is a B1,BT, BV then no, I'd not really trust it. A B3, yes, you should be fine.
General rule of thumb is that if a psu does not have the necessary pcie connectors, it's really not designed for the gpu power needs. I'd not trust a 750w psu with only a 6pin pcie for example.