Oswald used his first bullet for the indispensable requirement of zeroing (sighting-in) his reassembled weapon.  He gave himself one round and about 10 seconds.  Could he do it?

(1) The captain of my high school rifle team could usually zero a rifle in one shot.

(2) Even without the rigorous Marine Corps training in rifle marksmanship that Oswald received, if it takes you more than five seconds to do this, you have my sympathy.  :-)