They also needed refueled after takeoff to replace the lost fuel. Here's a Google AI blurb on that:

The SR-71 typically required one aerial refueling immediately after takeoff (roughly 7–15 minutes into the flight) to fill its tanks for a mission, which was necessary to support the immense fuel consumption required to accelerate to Mach 3+ and reach altitudes over 80,000 feet. This initial, crucial refuel topped off the fuel lost from ground leakage and the high burn rate during ascent.