Three things only to consider. Low limit (innermost extent of movement) high limit (outermost) and cable tension. If you haven’t got enough cable tension it won’t matter how far out the upper limit is, the cage just will not get there.
New derailleurs come with a block for pre-tensioning the mech. If you haven’t got one, just drop the derailleur onto the small ring, and then move it out a bit by hand, then jam something between the mech and the down tube. Make sure the barrel adjuster on the shifter is 2-3 turns out from fully in. Disconnect and reconnect the cable, taking all the slack out. Now remove your ‘block’. You now have a mech with too much cable tension, but the ability to adjust it out. This is far easier than trying to add tension via the barrel adjuster.
Mech limits and band height should both be set before connecting any cable!
I’m still getting all three rings with my knackered front mech. It slops all over the place when you waggle it by hand, but with some cunning manipulation the front mech is easier to bodge as it is far less sophisticated than the rear.
Good luck.