Core GM 650 comes with two PCIe (8/6 pins) power cables. Try with another PCI-E power cable and look if you can fully seat it.
except for the little lever on the PCIE cable itself
This doesn't get into the way, unless you try to plug the cable in upside down.
Couldn't find good video on connecting 8/6 pin to GPU but here's Steve showcasing how to connect the new 16-pin (found on all RTX 40-series GPUs) to a GPU. At 13:04:
View: https://www.youtube.com/watch?v=_QmKYJzJhB4
Same method holds true for your 8-pin socket as well. You need to hear a small click, for PCI-E power cable to be socketed fully.
Now, if the 2nd PCI-E power cable that you PSU has, also doesn't want to seemingly seat fully, then issue is most likely with the used GPU that you bought. Since Seasonic build quality is really high and i have yet to see any of their cables and connectors being faulty (i've also used in total of 5 different PSUs from Seasonic, spanning from different eras and series, while i'm currently using 3 Seasonic PSUs).
But bad power connector on a used GPU is quite common to see.