Dumbbell work instead
Without access to a barbell, I'd dramatically change the programming from what Starting Strength offers, using dumbbells as heavy as possible for as few reps as possible. I'd have to give up on the heavy squats and deadlifts that really make novice linear progressions work, but that's OK. I'd focus on general athleticism, meaning that some of the strength work that we could get with barbells but can't with lighter weights will be substituted with conditioning and speed work. Once you transition to barbells you'll be able to focus on pure strength, and will hopefully be well prepared by the dumbbell work.
There are a wide variety of dumbbell exercises I would choose from, but I expect that I'd want to focus on the ones with which I could still challenge maximal strength: short farmer's walks, overhead presses, bench presses. I'd also make sure to get in some cleans, swings, and snatches. With all of these, I'd shoot for sets of three to five, but if the weight is sub-maximal I'd settle for more.
Targeting the lower body with less weight
One concern is that the lower body, being much stronger than the upper, will naturally be harder to challenge with maximal loads. One way to work around this is to use single-leg exercises like lunges, pistol squats, loaded step-ups, and single-leg deadlifts.