"Later studies indicate that the top cruise velocity that can theoretically be achieved are a few percent of the speed of light (0.08–0.1c).[17] An atomic (fission) Orion can achieve perhaps 9%–11% of the speed of light. A nuclear pulse drive starship powered by fusion-antimatter catalyzed nuclear pulse propulsion units would be similarly in the 10% range and pure Matter-antimatter annihilation rockets would be theoretically capable of obtaining a velocity between 50% to 80% of the speed of light. In each case saving fuel for slowing down halves the maximum speed. The concept of using a magnetic sail to decelerate the spacecraft as it approaches its destination has been discussed as an alternative to using propellant; this would allow the ship to travel near the maximum theoretical velocity.[18]
At 0.1c, Orion thermonuclear starships would require a flight time of at least 44 years to reach Alpha Centauri, not counting time needed to reach that speed (about 36 days at constant acceleration of 1g or 9.8 m/s2). At 0.1c, an Orion starship would require 100 years to travel 10 light years. The astronomer Carl Sagan suggested that this would be an excellent use for current stockpiles of nuclear weapons"
https://en.wikipedia.org/wiki/Project_Orion_(nuclear_propuls...
The fastest object we've sent outside of the gravitational field of the Sun would take about 75,000 years to reach the nearest star (if we pointed it at it). For perspective, the last glacial advance started in earnest about 75,000 years ago. We don't have any technology that can maintain an automated craft for that long, let alone life support for sentient creatures. Hell, our current technology is insufficient to permit a self-sustaining colony on any other planet or satellite.
Ultimately, the Fermi Paradox is based on the assumption that, given enough chances, an unlikely event is basically certain. While this is true, to do a proper analysis, you do need to look at orders of magnitude to see if there really have been enough chances. And we have so little information to base the computations on that the dominating term is your priors: if you think we ought to have seen alien life by now, you'll pick priors that suggest life is quite likely and find that we ought to have seen it; if you think we oughtn't, your prior will reflect that.