The Telegram apps support SOCKS5 proxy servers. Here is a list of free SOCKS5 proxy servers. In case you are looking for a more reliable SOCKS5 proxy service, you may want to try out paid services.
Nice companies offers some trial (e.g. a week or something). Forget about the no logging policies. Since you do not have full server access, you are unable to check it. See the proxy/VPN as a way to be able to connect to specific services (in case you are blocked).