Building a Computer in Jesus's Time

Perhaps not exactly what you have in mind, but there is the Antikythera mechanism [0][1], the first known analog computer, dating back to about 100-200 BCE which exhibits gear-work that one doesn't see for another 1500 years or so. The device calculates the phases of the moon and the motion of the known planets and more for any date over a 76 year cycle. It takes into account the retrograde motion of Mars, can calculate the dates of eclipses, etc. There are videos on YouTube showing how it is supposed to have worked, e.g. [2].

[0] https://en.wikipedia.org/wiki/Antikythera_mechanism

[1] https://www.age-of-the-sage.org/archaeology/antikythera_mech...

[2] https://www.youtube.com/watch?v=ML4tw_UzqZE

Given limited technology and the desire for something electric and programmable I think your best bet would be a relay computer. Konrad Zuse built the Z1 entirely out of hand-cut sheet metal strips in his parents' living room:

https://en.wikipedia.org/wiki/Z1_%28computer%29?wprov=sfla1

That said, you would need lots of flexible ferrous metal and a source of electricity, probably large voltaic piles. And you would need to find a way to produce and insulate large amounts of wire.

Well... Wikipedia, in the article on glassblowing, says that the earliest example came from Jerusalem, dated from 37 to 4 BC.

Making the metal parts was well within their power. At least the shapes, though maybe not the alloys that we would use. Getting that shape inside the blown glass might be harder, given the tech of the day.

Getting a vacuum in it might be the hardest step. In fact, I don't know that it was possible at all, given the tech they had available. The first vacuum pump was in 1654.

If you suddenly went back in time, you would be floating in vaccum of space millions of miles away from Earth, so the answer is probably no.

There are several appropriate times in history when the necessary details were aligned for rapid (<200 year) progress from basic manual labor industry to advanced manufacturing. I assume that a mechanical pre-computer like Babbage's difference engine, rather than a fully reprogrammable electrical system, is acceptable.

Certainly within the history of China, India, and various African, Greek, and Middle Eastern cultures, complex mechanical devices with sequencers and even primitive logic gates were being implemented. See, for example https://en.wikipedia.org/wiki/Ismail_al-Jazari as well as https://en.wikipedia.org/wiki/Tang_dynasty#Alchemy,_gas_cyli... as examples where societies combined the necessary wealth, stability, education, social and religious culture to build very impressive mechanical devices.

I'm going to assume also that you have The Knowledge (https://www.amazon.com/gp/product/B00DMCV5YS) all the way up to basic electronics.

At that point you would have everything required to gather people and money and time to build a relay- or vacuum-tube based computer. I recommend reading the early sections of The Idea Factory https://www.amazon.com/Idea-Factory-Great-American-Innovatio... describing what the early Bell Labs was like. Many modern innovations came from itinerant scientists who interned at Bell Labs, learned to make vacuum tubes by hand (IE, blowing air precisely into molten glass, and sealing the various electronics in place) and then left to found companies that utilized tubes (for example, Beckman went through this process and used the acquired knowledge to build a vacuum-tube based amplifier which was critical to the modern pH meter).

Now, a few challenges. Since you're just dropping back into a society that hasn't undergone an industrial revolution, you don't have a bunch of useful cross-supporting things like a healthy industry that makes high quality alloy steel for you, or optics companies which design and sell sophisticated lens assemblies for high quality telescopes to debug your work, or electronics companies pumping out millions of standard resistors with tight variances, etc. Without those, many steps that would be trivial would instead take extended time. Also, the absence of a statistical quality culture (see Deming) and the fact that most components will be built by hand by artisans means that your computer will not be very reliable (producing incorrect results, or breaking often).

On top of that, you'll probably face skepticism because your early computers won't be able to do anything useful compared to skilled humans. You would probably do best by finding a local military leader and convincing them you could help with ballistics calculations...