Remember the Doctor's words in Rise of the Cybermen: "It used to be easy. When the Time Lords kept their eye on everything, you could hop between realities, home in time for tea. Then they died, and took it all with them. The walls of reality closed, the worlds were sealed. Everything became that bit less kind."

If travel between universes is getting easier again, it could be a sign that Gallifrey is returning.

(A variation on this would be a pre-Time War Doctor travelling to our reality, and meeting a NuWho fangirl who refuses to believe this idiot in a long scarf is really the Doctor until she sees Sarah Jane with him.)

Or...

Perhaps the TARDIS has been sent to this universe by someone who doesn't care what this does to the fabric of space.

Missy and/or Davros (depending on which, if either, is alive at the end of tonight's episode) sets a trap for the Doctor. Detecting the approach of the TARDIS, and unable to destroy it, they open a wormhole in its path, sending it to our reality. Then they close the wormhole behind, trapping it and the Doctor here.

(You could begin by showing this, then pulling back to reveal that it's the cliffhanger ending of an episode the fangirl protagonist is watching.)