The 11th Doctor needed to do Damage Control before the Daleks escaped.

Their only advantage being the Time Lords got pulled inside the 25th Century Star Trek Universe by the Q Continuum beforehand.

The Planet Gallifrey got Federation Membership out of instant desperation.

Pulled out of the Time War into another dimension, the Starfleet Technology quickly saved them from starvation.

Their only disadvantage was everyone had Warp Engines and the Time Lords didn't.

The Time Lords were instantly helpless against everybody and Reverse Engineering Starfleet Technology to defend themselves because of it.

So now the 11th Doctor's TARDIS had it's own Warp Core and Warp Field Generator integrated within itself.

Thankfully the Q Continuum welcomed the Time Lords seeking to test how the Federation reacted towards their war with the Daleks.

The Daleks changed the Temporal Cold War for the better, all the factions stopped fighting among themselves to deal with the Daleks.

The American Republic

22nd Century Time Travel Faction seeking to Escape World War Three.

Point of Origin: Parallel Timeline where Humanity never made First Contact with the Vulcans and Developed Warp Engines during the 23rd Century.

Parallel History: The Romulans Conquer the Vulcans and Humanity goes into hiding to avoid them.

Obviously having Humans jumping between dimensions trying to reshape history would lead towards problems before the Daleks forced everyone into working together.

So naturally the Q Continuum welcomed the Time Lords into their playground of Duplicate Civilizations to see what happened next.

Duplicate Planet Earth Civilizations from other dimensions trying to survive under Starfleet Protection seemed to be the repeating theme.

The Time Lords debated how to avoid getting involved.

The 11th Doctor got pulled into the Star Wars Universe.

Suddenly the 11th Doctor was Giving Food Replicators to Emperor Palpatine and the Klingons were Helping Count Dooku against him.

The Q Continuum was very amused.

The Time Lords were irritated at the Star Wars Universe merging with the Star Trek Universe around them.

What If Universes.

What If Starfleet got assimilated into the Borg Collective.

What If Starfleet created the Borg Collective.

What If Starfleet became the Q Continuum and everything was duplicated for their own amusement.

The Time Lords frowned, Starfleet creating the Borg and dooming themselves inside other dimensions didn't amuse them very much.

It was an endless circle of Starfleet destroying themselves while the Q Continuum watched.

Somehow the Q Continuum Sending Starfleet to stop themselves from creating the Borg within another dimension made sense.

The Q Continuum probably told Starfleet how to create the Borg to see what they did and now the Borg were spreading into other dimensions unchecked.

Some dimensions got assimilated by the Borg and the Time Lords were all outmatched by the Borg themselves.

The Q Continuum were instantly dumbfounded how the Time War crippled the Time Lords beyond what they expected.

So now the Time Lords were rebuilding before the Borg wiped them out.