For sure you won't get if if you don't try. I am not going to say it is impossible, but it is improbable. Again, let me reflect that you need muscle tone to do this. It takes 6 weeks to add to tone, and that is if you do it right.
Let me ask this question, would you expect a weight lifter that can press 200 lbs to lift (without a spotter) 300 lbs in 6 weeks? That is quite a demand. And to do this without straining or pulling muscle is the other risk that must be balanced. If the 6 week goal was to get to 225 lb, then a much higher chance of achieving this would be seen.
So can you get a solid D range to an G in 6 weeks? That is an audacious goal. I do believe the E can be achieved, and perhaps the F, but another whole step to G is quite a task to achieve in 6 weeks, based on the training of muscle to support such a demand in such a short time.
To say it is impossible, I cannot go there. Here is what I suggest doing. Try to find the slurring studies of Cat Anderson and start working on these. Also, in between practice, take your mouthpiece and play it into a hand towel. Do this a half hour, twice a day. For the majority of the time (75%), take you mouthpiece towel range to that C. Then the additional time, start working the mouthpiece towel to above the C.
The reason for doing this is to train your lips to perform at a resistance much greater than you will feel when you do this with the horn. In so doing you will not only develop strength, but also the feeling of not having to push so hared once you remove that resistance (going back to the horn). This also trains you to RELAX once you are back to your horn with more muscle strength. RELAXING is just as important to prevent you from intuitively straining to put additional force you really don't need, and will only serve to close off your airflow.
So good luck and do keep us updated.