As @dsaxton said, you can build a discrete time model. You set it up to predict p(fail at this day given survived up to previous day). Your inputs are current day (in whatever representation you want) eg one hot encoding, integer,.. Spline... As well as any other independent variables you might want
So you create rows of data, for each sample that survived till time t-1, did it die at time t (0/1).
So now the probability of surviving up to time T is the product of p(don't die at time t given didn't die at t-1) for t=1 to T. Ie you make T predictions from your model and then multiply together.