Thankfully, there are many providers who have special programs or discounts for nonprofit websites and other nonprofit design projects. You can always email to ask for an organization’s nonprofit pricing if it is not easy to find on their website.
Many options (including trials) are free. Just be sure that you will not grow out of the free option anytime soon, and when you do, the paid version will include everything you need, and the costs will fit within your budget for 6-18 months.
Also, make sure to ask your prospective provider what they are doing about diversity, equity, and inclusion. Ask about their team and if they hire diverse staff.
Online Impacts (website design, social media)
CrowdSpring (Give Back program for design)
6 Best (REALLY FREE) Website Builders for Nonprofits in 2020 (article by Website Planet)
Canva for Nonprofits