Yes and no. It's relatively easy to avoid the blast, if you have the money to spend making it happen. Bunkers are an obvious choice. How long you stay down there depends a lot on what was dropped where. One bomb a mile away? You can leave in a day. Global nuclear apocalypse? It'll be a while.

There were many, many nuclear proof bunkers and locations made during the cold war, on all sides. Its not particularly difficult to build something capable of surviving a nuclear detonation, often these would be built underground or in the side of a mountain. There are many, many of these facilities, both civilian, military, and government though today, most are abandoned or used for storage.

Nuclear weapons are extremely powerful, but we also know an absolute ton about how they work and figured out its not that hard to build shelter or even whole facility to survive an attack.

The lingering question though is when will it be safe to get out of the bunker, as there may be radiation, although this depends on the specific weapon used and where it detonated.

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.

What makes nuclear war so complete is what they call M.A.D. mutually assured destruction. Many countries had or may still have systems that when a nuclear launch is detected they counter launch their missiles in case they don't survive.

A single nuclear missile has a blast zone of certain fatality then rings spread out to estimate the levels of destruction. After the initial blast there will be a radioactive fallout cloud that moves. That cloud will eventually dissipate. I read an article once that claimed a fallout cloud is only lethal for about 12 hours and it's best to shelter in place to avoid direct exposure. But take that as unsourced because I don't remember where I read it.

In the mid-20th century people did have fallout shelters installed on their property. It was like a tornado shelter but sealed up much better. A Brendan Frazier movie called Blast To the Past has a really neat fictional one as a set piece. If you're not in the blast zone and the other nuclear powers haven't launched all their nukes then a fallout shelter is very practical. That information is also anecdotal since I don't believe they ever actually tested it out. Somewhere there is a website that simulates a nuclear blast and the damage zones overlayed onto a map.

So a nuclear attack has three components to its deadliness. One is the initial blast. Anything at the epicenter is vaporized. Anything within a given radius of the epicenter is blasted away, depending on the power of the weapon. Second, everything catches fire and this multiplies the damage. Third, which is less of a factor now that nuclear weapons use their fuel more efficiently, is fallout. Depending on the amount, it can make entire areas uninhabitable for quite some time. With one or two bombs, as seen in Japan, those areas can be habitable relatively quickly. But, say, total nuclear war? That's an entirely different scenario.

Now, a nuclear attack is likely to be centered around major population centers. You're pretty much screwed if it comes to pass. But if you're far removed into rural territory, you could manage for quite a while given that total war doesn't cause a nuclear winter. The other issue would be the aftermath of such an attack on things like electricity, water sanitation, supply chains for food and supplies, the environment, etc. We could literally bomb ourselves back to the stone age of which the recovery takes centuries.

In short: one bomb? So long as you're a couple feet underground and removed from the immediate area. A full nuclear exchange? You're probably screwed either immediately or eventually.

Sure you can survive a nuke, just dont be TOO close to the blast and then stay out of the radiation for like 80 years.

And ofc have water, food and everything else you need

There were many people who survived the bombings of Hiroshima and Nagasaki, although most are dead now (and not necessarily of nuclear-related reasons).

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