Disconnect the linkage from the trans (pinned rod and ball/cup connection) and then manually select 1st gear. You can select it, then unhook the linkage as well.
Anyway, once the linkage is off, make sure the trans is fully selected in 1st gear.
Hop in, press the clutch, start the engine, and try pulling away.
If it pops out of gear, there is damage inside the trans, or something with the selector.
If it stays in gear just fine, the linkage is pulling it out of gear under load.
It could be a linkage alignment issue, it could be bad engine mounts allowing the engine to move and pull the linkage tight.