The sources
וּשְׁמַרְתֶּם אֶת חֻקֹּתַי וְאֶת מִשְׁפָּטַי אֲשֶׁר יַעֲשֶׂה אֹתָם הָאָדָם וָחַי בָּהֶם
Shmuel in Yoma (פ״ה ע״ב (85b)) expounds: "live by them - and not die by them".
SA (OC 328:2) rules: one who hurries to desecrate Shabbat to save a life is praiseworthy; one who stops to ask is a shedder of blood. Even doubtful danger - one desecrates.
Proof of the value of speed: halakha prefers that leaders of Israel do it, not non-Jews - so Shabbat never appears as an obstacle to life.