When pressing in the axle, ensure that the bearings are not pressed out again by supporting the bearings.

Use a spacer that can hold in the bearing, but allow the axle to be pressed through.

You can 3D print such a spacer, or use the outer ring of the replaced bearing (ground down to prevent press fit).

Place the spacer.

Let the spacer push on something, a large socket for instance, and center it on the press.

Press in the axle until the retaining ring groove is above the bearing (and the retaining ring can be put back).