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Is there a time system that two spacecraft traveling in different galaxies could share?
For example, a spacecraft jumps to an unknown location in the universe, far away. How could they synchronize? Or know the “universal time”.
For time measure there is something perfectly accurate such as a photon clock.
First of all, simultaneity is an ill-defined concept in the modern understanding of the universe, so realistically, the question can be answered with a simple no.
Second of all, I'll assume we're talking different (and arbitrarily distant) galaxies in the same universe. When you bring in multiple universes, there's no good reason to assume the time dimension's arrow would be parallel and pointing in the same direction, so comparing times across universes wouldn't make much sense either (imagine one universe's time arrow as perpendicular to the other --- this actually happens inside event horizons of black holes.)
But let's try to avoid answering no, because that's boring, right? Let's imagine some partial workarounds. On earth in the distant past, sailors would determine their position with reference to the stars. In the universe, you can use the temperature of the Cosmic Microwave Background to know how long it's been since the Big Bang, since it will decrease as time passes and the universe expands. With sufficiently accurate measurement, you can get arbitrarily precise results (down to a certain limit).
Under a Newtonian framework, that would be a universal clock. However, in the real world, two observers using the CMB clock will assign perfectly reasonable times to a distant event (say observer A 'waving' from his galaxy to observer B on Earth), with the slight snafu that the times won't actually match.
With the theory of relativity currently being much depended on and not being proofed wrong, time is very subjective and depends on the condition of the observer. I suppose what you means is the approximate time that every stationary or slow-moving object tells you it is, perhaps a clock back on Earth. I believe your problem in the question is that photons travel at a fixed speed which seems insufficient for intergalactic synchronization purposes.
This superficially seems analogous to the time delay caused by low network speed when sending or synchronizing data(time, real-time computer game data, video calls, etc), called latency. As implied by the time precision needed by modern activity, time synchronization network protocols have been developed to synchronize time while minimizing latency issues, including the NTP and PTP. However, intergalactic round-trip time is pretty much unacceptable and impractical.
If light cannot solve the problem, it seems like the only way to solve it is the superluminal "spooky action at a distance" as described by Einstein -- quantum entanglement. Quantum teleportation has recently seen some success. Yet, this is just another disappointment: relativity doesn't say nothing can move faster than light. It says no mass or information can move faster than light. We can instantaneously teleport quantum states, but real communication would have to wait, for as least the duration light needs to reach the target.
The final answer, there is still no means of communication faster than light. Maybe warping spacetime might help? Anyway, if your story is Sci-Fi, you could just say that they can create ultra-small wormholes and send information over that. It would certainly drain lots of power though.
Well, still using the clock. I know this answer problably isn't good, but if Team 1 go to an galaxy and Team 2 go to another, is better they start to count the time of the trip, for example: "About an hour ago that we took off from Earth."
I might suggest something in the nature of quantum entanglement where in a central clock defines an arbitrary time that all dependencies then rely on with perhaps an offset like timezones based on distance from that clock at that time. Depending on the society at play it's not unrealistic to imagine a series of relays that are used to create a distant communication network that could also relay such information.
