Take a 74HC132 chip, it's four two input NAND gates but they have Schmitt trigger inputs so slow inputs can be used. One input is directly from your sensor, the second input has a series resistor and a capacitor down to 0V. So, the sensor output goes high, input one goes high and input two slowly ramps up to 5V over 1 second, after which the output of the NAND goes low.