How can I find orbital parameters for a sun-synchronous orbit?

Question

I would like to compute ephemerides for a satellite on a sun-synchronous orbit, starting with only the following parameters¹:

• altitude or inclination;
• local time of the ascending or descending node;
• starting date.

Using Orekit, I am able to compute ephemerides for a circular orbit given: the orbit radius, the inclination, the right-ascending node, the true anomaly, and the starting date.

I already know how to link altitude and inclination, and computing the orbit radius from these is trivial, but I do not know how to find the RAAN and the true anomaly given the above parameters.

I found this related question How Local time of a sun synchronous orbit is related to Right ascension of ascending node?, but there the answers do not provide formula to compute the required parameters.

Is there a way to compute the RAAN and true anomaly from the above parameters? Or another way to compute ephemerides starting only with the above parameters?

_{¹ I am assuming this is possible since it is how a sun-synchronous orbit is specified in STK.}