How can a PhD holder safely negotiate the salary level for a TVL E13 position?
First, talk to your future supervisor. If they do not support it, chances are slim. Or, if they say it is impossible, equally so.
If they support it: Find out what the rules are - well, probably your supervisor knows.
Generally, there are two options, depending on the place: Either, the administration decides on their own.  Still, they might not proactively put you  in a higher level, but wait for you to ask for it and supply documents proving that you have previous experience.  In that case, the support of your supervisor will certainly help the process. And it is not unlikely that the administration would ask them if they judge the qualification equivalent.
Second, it could be that your supervisor has to write a justification why you should get a higher level, and then the administration decides.  Certainly, in that case the support of your supervisor is essential.
Finally, it could be that the administration has very rigid rules on this, and the supervisor has no influence on that. In particular, they could have the rigid rule that they don't recognize anything which was not in German public service (that would be the most conservative option, since they don't have to vouch for anything).
Good luck!
(In any case, I would say that level 2 is realistic, since, it only requires &gt;1 year of experience. Level 3 is more ambitious, since it requires &gt;3 years of experience.  In any case, also check the salaries for the different levels - the steps are not uniform.)