A 403b is NOT by definition an annuity. A lot of them have annuities as some or all of the choices, but others do not.
Your HR department should give you a list of providers with contact information. Most of the insurance companies will offer annuities and/or have expensive mutual fund investment options. However, in your shoes I would call all of the companies except Ameriprise and Valic and get the investment options. Don't even bother to call Ameriprise and Valic. They are just plain awful plan providers. When you call, state that you are not interested in annuity options, and ask if they offer anything else. If they say no, or try to sell you the annuity, politely end the conversation and move on to the next company on the list.
My guess, based on the list, is that Voya will be your best option. However, you won't know until you make the calls.