I'll let the guys that do this stuff all the time give you more specific recommendations. I'm only about a year ahead of you in my experience with GSF in a new pond.
I can however relate some of the concerns I would have if it were my pond.
What are the largest size GSF? Don't want to purchase LMB fry and put them in the pond only to become an expensive GSF snack. A GSF can easily eat something one third its length, and longer if it has the right shape. Note the picture linked below. This is a small GSF I caught in a minnow trap. Some unfortunate FHM also entered the trap and the GSF ate him. I saw just the tail inside the mouth of the GSF and pulled that FHM out of the GSF. The minnow was about 2.5-3" long and you can see how long the GSF is in comparison to it. So you are going to need LMB big enough they don't get eaten by the GSF.
In our area the GSF would be done spawning for this year. Not sure about your location. So there will be no more new GSF added till next year, but the current ones you will grow some more this fall likely. One consideration might be the size of LMB fingerlings available. Are larger fish more available in the fall or spring in your area? Might make a difference. Not all sizes of stocking fish are available at all times.
If your stocking is going to be from catching fish from another BOW, then I definitely would start putting in big enough fish ASAP. But if you are going to purchase additional LMB at some point, don't want a few large LMB that will also be eating your new small LMB. Something to keep in mind if you have the desire to go catch some LMB and put in now to start working on the GSF.
These are just a few of the things that would be going through my mind and questions I would have. Now some of the experts probably have good recommendations of how to proceed.
