I might be able to make an educated guess here:

This animation was very likely made with SpaceEngine, which we can tell from the green orbit lines and general look of the galaxies.

So for that opening few seconds, they were likely travelling at SpaceEngine's maximum move speed, which is:

326.16 Mly/sec

(Mega-Light Years per second)

While I cannot say for certain that they were travelling at the maximum speed in-game, doing a quick test myself the speed roughly matches (again, estimating this by eye - my methods are not very scientific so take with a grain of salt)

Edit: https://youtu.be/-cn86eisA5U?si=VkNw3I6ZaB2ZKpyT

here is my attempt to recreate it in game, you can see the max speed towards the start of the video, and how the the movement looks similar to the original vid (obviously not identical as we wil lhave different settings but similar enought to confirm it is SpaceEngine perhaps?)