Drake should have added the time interval in which civilizations manage to survive, which may be a tiny fraction of the billions of years since the Big Bang. This time interval needs to loosely overlap with that of another civilization for them to be able to interact, even when it would take centuries to send signals with the speed of light. Look at mankind, maybe aware of the universe since the days of Newton, it’s already on the brink of extinction because of wars and climate change. To give you an indication of time relativity. If we would notice some time this year the explosion of the 10th brightest star in the night sky, Betelgeuse, then it exploded long before Isaac Newton was even born. If we scale down the approx. 14 billion years since the BB to one year or 365 days, modern man would appear only in the last couple of seconds before the clock strikes midnight.