If you pray the nafilah prayer, then that is the mustahab thing to do, to pray it on its time, and then pray the wajib prayer, and with doing this, you will not be deprived of anything.
You will gain the reward of the nafilah prayer, and the reward of praying on time, which in reality that is what you are doing.
Therefore, there is no need for you to pray the nafilah prayer before its allocated time.
For a person who has Qadha of obligatory prayers undone yet, Nawaafil and recommended prayers are permissible and valid provided it does not hold you or make you neglect performing your obligatory Qadha.
Your priority is fulfilling your wajib, and then turning to nawafil. If you were to pray your qadha` prayers during the time of your nawafil, you will also be granted reward as well. So, as long as you have qadha` prayers, you should not be doing nawafil, and with a good routine for qadha' prayers you will be able to finish it in an adequate time.
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