How can I factory restore Mac OS 8 without a disk?

A factory restore for a Power Mac 5260/100 would install OS 7.5.3, as was included on the original restore disk. For identification purpose only, that disk is listed at ebay with a $24.99 price tag. If you want to reinstall OS 8, the universal/retail (white) OS 8 installer disk would be needed.

Welcome!

I do not think so. The Recovery mode that can restore with only an internet connection was not developed until long after the 5260 was a fond memory.

However, consider emailing some Apple User Groups in your area. The group leader or a mod often knows a member who keeps track of old system disks sources. Often the mod will send members a "someone is looking for..." message to members when they have an inquiry. They maybe able to direct you.

This is the web page that lets you search for a group by area:

https://appleusergroupresources.com/find-a-group/