Obviously, I don't trust Google translate, or I wouldn't be here.
Just to clarify:
By "The will", I mean "a deliberate or fixed desire or intention".
You are indeed right not to trust Google Translate with Latin.
I recommend translating "will" with voluntas. I don't know a better word for this purpose. Please check the linked dictionary entry to see what nuances it has.
When translating constructions like this to Latin, I suggest using the genitive of the gerund. If you want to describe the ease of singing (facilitas canendi) or the joy of drinking (gaudium bibendi), this is a good way to go.
I therefore suggest voluntas vivendi, which also happens to sound pleasing for several reasons. Translated literally to English, it means "willingness of living", but that is not as idiomatic English as your "the will to live".
Schopenhauer himself rendered his concept "Wille zum Leben" as "voluntas vivendi" in a marginal note to Augustine's Civitas dei.
A touch more positively than Joonas's answer, I suggest studium vitae, 'zeal' or 'eagerness for life'.