If Telegram is not opening, the quickest fix is usually a VPN. A VPN routes your internet through another country, which can bypass local restrictions. Install Proton VPN or 1.1.1.1 by Cloudflare, tap Connect, and then open Telegram again.

Telegram also supports MTProto Proxies, which work directly inside the app. Open Telegram → Settings → Data and Storage → Proxy Settings and enable it. You will need a proxy Server and Port, which you can find by searching "Free MTProto Proxy Telegram".

You can also try changing your DNS settings. This helps if your internet provider is blocking Telegram through DNS.
Android: Settings → Network & Internet → Private DNS → Private DNS Provider Hostname → enter dns.google
iPhone: Settings → Wi-Fi → tap the (i) next to your network → Configure DNS → Manual → add 1.1.1.1

If Telegram still says "Connecting...", try these quick fixes:
• Switch between Wi-Fi and Mobile Data.
• If using a VPN, change to a different country server.
• Turn Airplane Mode on for 10 seconds, then turn it off.
• Use Telegram Web in your browser if the app is not working.

Useful links:
Proton VPN: https://protonvpn.com
1.1.1.1 by Cloudflare: https://one.one.one.one
Telegram Web: https://web.telegram.org