I am just beginning with amateur radio and would like to start with an entry level handheld transceiver. I would like to consider manufacturers based in the United States, but I have not found any. Are there any USA handheld ham radio manufacturers?
Motorola is a US-based manufacturer that makes handheld VHF/UHF transceivers, but they are intended for business and/or government use. Many models can be programmed for amateur frequencies though; programming usually requires a special cable, a computer, and programming software. Compared to models aimed at the ham market the Motorola models lack many features, like the ability to scan band ranges, but if you just want to talk on a few repeaters, a Motorola HT capable of "wide" FM on the right band(s) should work fine. They are quite a bit more expensive than the usual popular ham models, but on the other hand they are considered very rugged. I looked around on eBay to see what was available, and the model I found had been made in Malaysia, but I would think that older and/or more expensive models were made in the US. The future of business and government two-way communication is digital modes and/or "narrow" FM, so you would probably want an older model anyway.
If you are truly determined to get a US-made HT, your best option is probably to find someone in your local club who is a current or retired two-way radio dealer who knows Motorola models, can easily get the right model (which might be used), and can program it for you. (We have such a ham in my local club.) You might be able to do it on your own, but you'd have a steep learning curve. Either way, be prepared to spend quite a bit more than you would for a typical Japanese-made or Chinese-made ham HT.
Are there any USA handheld ham radio manufacturers?
Sure, I found the below link by simply searching using my favourite search engine.
You may consider RELM Wireless
[Edit 15-Jan-2021] It seems that the RELM website is now redirecting to https://www.bktechnologies.com/
I am just beginning with amateur radio and would like to start
Be prepared to fork out some serious money if you limit yourself to US based manufactures only. Compare the prices with a Chinese HT which purchase price is around $30...
Example: I found the DHP model from RELM Wireless retailing at more that 2000 dollars. This model has obviously more features than a $30 Chinese HT, but if you are starting, and want to get on the air, then specifically looking for US based manufacturers is probably going to limit your experience of the hobby.
You will probably find that many experimental electronics to supplement your HT, as well as DIY projects described on websites or magazines, will be very limited for US manufactured kit. This is simply because Japanese or Chinese kit is so much more popular.
Getting support/assistance/help for popular kit is relatively easy, you can always find someone who has a similar kit.
Personally I do own a Motorola, but it is a nightmare to program, the programming software and cable is closely guarded and not simple to purchase. I did manage to get it from Russia.
I would like to consider manufacturers based in the United States
Best advice I can give you: please reconsider.
Baofeng is not a US manufacturer but there UV-5R is a good entry level radio. That is the the only radio I have. It is not the best radio but it is cheap and easy to program. The downside is that they use different connectors than other radios which means it can be a little hard to find accessories.