Is it possible. Yes. Is it possible for you personally? Maybe.

The US government have facilities that are effectively impervious to nuclear attack. These bunkers are deep underground with complex ventilation and supply storage, and would house the critical functions of the US Government and Military in the event of a nuclear war.

Obviously you probably could not afford to do that. Instead you are probably stuck with at best a concrete and steel bunker only a few feet below the earths surface, with only basic ventilation and water/supply storage.

For you, could you survive a direct nuclear attack? Probably depends on your ventilation system. Since you’ll need a way to let fresh air in. Maybe you can design/buy a system that can withstand the pressure wave from the nuke, maybe you can’t.

But surviving a direct nuclear attack in a backyard bunker is probably unlikely.

BUT, if you aren’t at the direct epicenter, yes you totally could survive. Underground in your bunker. You’d have to stay down there for at least a few days, but ideally you would want to have a radio that you could listen to emergency broadcasts with (Yknow that really annoying TEST message that plays on radios and TVs? Yea, that’s partly for alerting people what to do during nuclear way)

Because it would also depend on things like the wind and where you live. For example, if the wind is blowing from your bunker towards the nuclear blast center, it’s blowing radiation away from you, meaning your area would be safer, quicker.