Can you beat the final singularity without Saints Quartz or Friend Points summoning?

Realistically, no.

Unrealistically, if you're insanely lucky with Necromancy CE on either your servants or a support servant.

This means that the only servants you get are Mash, the servants you get for clearing singularities, support servants and servants you get from finishing events. This also means that the only Craft Essences you get are the ones from events.

While there are many great servants and CEs you get from events. Actually clearing it with only your starter Servants/CEs is difficult even with a powerful support.

Finally, if it is possible, how long do you think it’ll take?

Don't try it.