There is a well known machlokes between Rav Moshe and Rav Shlomo Zalman which they both have elaborate teshuvos on, regarding paramedics and EMT's who went on an emergency call whether they can drive back home on Shabbos. Rav Moshe (Igros Moshe, O.C. 4:80) permits them to return home based on Tosafos understanding of the end of the Mishna 44b. The Mishna says - כל היוצאים להציל חוזרין למקומן. Based on the context of the Mishna we are speaking about those who left home with the "permission" of the Rabbonon so that they can tend to a pikuach nefesh type situation, and returning home would violate techum and also violate carrying their weapons. The gemara permits them to even carry their weapons home. Tosafos explains that the nature of this heter is התירו סופן משום תחילתן. We need to permit them to return home, otherwise they are not going to go at all. Tosafos says that only reason that this isn't listed among the other התירו סופן משום תחילתן in Beitzah 11b is because in each of those cases there is some other justification to permit it and it's not clearly permitted due to התירו סופן משום תחילתן, whereas over here it is obviously only permitted for that purpose and isn't considered much of a chiddush. Based on this approach, Rav Moshe understands that although all the cases in Beitza of התירו סופן משום תחילתן, only violate a Rabbinic prohibition, we learn from our sugya that we apply the concept even to permit the violation of a Torah prohibition since by not doing so there is a risk that one will not go to save lives.
Rav Shlomo Zalman (Minchas Shlomo 8) after asking permission from Rav Moshe to publish his disagreement (which is a great tzidkus on his part) has an elaborate teshuva where he shows from the gemara that Rav Moshe is taking the Tosafos too literally. The gemara explains that the last line in the mishna - כל היוצאים להציל חוזרין למקומן is actually not permitting one to travel further than the 2000 amos (at least in a case where the Jews have the upper hand). The Mishna is only permitting one to bring their weapons with them wherever they go, because by leaving their weapons behind, they wouldn't be prepared to ward off a counter attack. The gemara implies that there is no heter סופן משום תחילתן, rather the heter is for the סופן itself which is a case of pikuach nefesh. Rashi writes explicitly that when the gemara answers שחוזרין בכלי זיין למקומן, it means to say that they are stuck in the 2000 Amah radius of where they end up, just that they are entitled to take their weapons with them and don't need to leave it there. Therefore, there is no source from which to draw that we can apply the concept of התירו סופן משום תחילתן to even permit an issur d'oraysa.