Can I enter the USA from mexico, by car, without a passport, if I am 16 years old and a citizen? I am traveling for a missionary trip

The requirements for Americans entering into and returning from Mexico are here. Notice that they say you are required to have a passport to return to the US if you are 16 or over, and if you see Mexican immigration they will want an American to have a passport too. And these days it isn't possible for a 16 year old to get on an international flight to anywhere without a passport.

Unless you also hold Mexican citizenship, then, I'm assuming you aren't worried about getting into Mexico since you are planning to travel across the land border and won't be travelling beyond the border zone(?). This plan will probably work in practice if you stay close to the border since no one will likely ask to see your passport, but I'm pretty sure you are still supposed to have a passport with you to identify yourself even there. Also, the US won't actually deny entry to a bona fide US citizen (what if you lost your passport instead?) but they may make you spend a long and painful wait at the border while they satisfy themselves that you are indeed a US citizen.

So I wouldn't go so far as to say you absolutely couldn't make this trip, since there may be no one who would keep you from doing so, but you would be knowingly doing enough things wrong that I wouldn't do it. You really need the passport.

U.S. Citizens must use a passport book if entering by air, but can use any of the following if entering by land or sea: U.S. Passport; Passport Card; Enhanced Driver’s License; Trusted Traveler Program card (NEXUS, SENTRI or FAST); U.S. Military identification card when traveling on official orders; U.S. Merchant Mariner document when traveling in conjunction with official maritime business; or Form I-872 American Indian Card, or (when available) Enhanced Tribal Card. Western Hemisphere Travel Initiative

However, as others have mentioned, Mexico requires the passport book for all except limited locations within the country (along the border).

You do not need a passport. I go once a month to pick up random pharmaceuticals... All you need is state I d or driver's license, military ID. Birth certificate, and I bring my SSN card. I ha EA been doing this once a month for the last 8 years. 2009 to 2017.. never had to go to secondary I spection. They type some stuff on computer, I give them a list of prescription s. And they say welcome back. And I drive right through. Every month for 8 or 9 years.

If you can satisfactorily prove your US citizenship, you cannot be denied entry to the US.

What proof of citizenship do you have? US birth certificate and a photo ID? You will probably be detained for a while while they check out your citizenship (especially since there are many fake birth certificates), and they will at least give you a stern lecturing about needing a passport. It should not be something you do unless you have no other choice.

Also note that you can apply for a US passport at a US consulate in Mexico, if there is enough time to do so.