The solution was to come up with a circuit that would output gpio2 = Vcc - Sensor output. This will keep gpio2 normally high. When the sensor triggers, it will be pulled low. Then, your software can be set up to look for the LOW on gpio2. Since my ESP-01 boots before the sensor device ever sends a HIGH, this works very well.
The circuit uses 4 1K resistors and an Op Amp. I also put a 47K resistor in between gpio2 and my HC-SR501 sensor device.
Here is the circuit:
If anyone else has a solution, please share it.