How do I reinstall the glass dome on my light fixture?
Without being able to see the clips, I’m still going to say to try placing the lip of the glass cover against two of the clips and then press against the opposite side of the cover: use the cover to press in the clips. You can then use your other hand to press in the remaining clip.

You may actually find that one of the clips is fixed. In this case, use the cover lip to press in the two mobile clips, raise the cover to fit under the fixed clip and then release pressure to let the cover lip slide into the fixed clip.