Build a university/engineering school
As many answer have pointed out, building a gun from scratch in the bronze age will be very difficult. Thus to solve this you should not try to build a gun, but build a society that can create a gun.
So in your backpack bring knowledge, USB sticks with encyclopedia and all textbooks you can get your hands on from primary to university grade. This should not take up a lot of space. Bring 4 laptops with the devices to charge the laptop, solar panels and converters. Bring enough to have some spare. Bring some actual guns for protection from the locals if necessary and to impress them. Last and most important bring detailed start up plans and tools. Since it is the bronze age, I would suggest bringing steel axes and saws, hand drills and if still room left maybe steel screws for easy construction. Also fill the rest of the bag with gold/silver/diamond or whatever currency the locals use. I am assuming a rather large bag pack, but you can reduce all number to one (2 for the electronics) if it does not fit.
Once you arrive in the past you need a place to settle and build your university, convince the locals that your knowledge is worthwhile and get as many pupils you can support. If you can choose the place you land make sure your near coal, ion and oil deposits. A place with some kind of states already in place might be best, see: Bronze Age States, but you might also opt for advanced framing cultures. The hittites empire might be a good place to locate (modern Turkey, Anatolia), near lake Van seems to have all the necessary resources, I just don't know how far underground. Resources: metals, oil and coal.
Once you arrive roughly follow the next steps:
1. Sell you knowledge for food/influence. Best knowledge to sell is probably improving tools (mainly agricultural) and health treatments. Distilling alcohol might also be a viable option or construction work.
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Build/Buy a house/school and build a printing press. Start printing the correct books for the school. So learning how to read, simple arithmetic and than basic engineering principals. All in a very directly applicable manner.
3. Start gathering and teaching pupils and spread your influence. Do this by helping the local community and state community and let your pupils do projects.
4. Start building a foundry inside your school and start making bronze tools. Don't overlook the fact that you probably can improve their bronze making a lot. Being very valuable, also you can teach/use local bronze smiths to speed up you foundry.
5. If no iron is available make a project of building one, you need to have the exact location of easily accessible iron available. Remember that you only need small amount, so no need to look for the very big mines of nowadays.
6. Progress from bronze to making iron tools
7. Later progress to weapons and a weapons factory.
8. If oil is available one might make plastic in a very early state. Making some kinds of plastic is not that hard and has very good material properties for tooling compared to the wood that they would normally use.
This plan will take quite some time and in the mean while you need to make sure that both the local and state community are cooperative and appreciative of you. Building a society by cooperation is probably easier that force, but make sure you have enough force to withstand outside pressure. Have better weapons and tactics should allow you to withstand a lot of pressure if necessary.
To speed up the whole process supplying the state with better weapons and tactics than the enemy can boost the whole procedure of creating a weapons factory. In that way you could start with a primitive weapons factory and gradually upgrade to a modern one. 222