Forward your company's address to your Tuti support address, so emails to it land in the Inbox. Both are in Settings → Inbox and email, under Your own address → Receiving emails, each with a copy button. On the Free plan, copy your support address from Email → Your support address on the same page. See Set up support email for the rest of the setup.
Cloudflare Email Routing is free when your domain's DNS is at Cloudflare. It also works when nothing receives email for your domain yet: turning it on adds the MX records it needs.
Forward it
In the Cloudflare dashboard, open your account's Email Routing → Destination Addresses and add your Tuti support address.
Cloudflare emails it a link. Open it in your Tuti Inbox and choose Verify email address.
On your domain's Email Routing → Routing Rules, choose Create routing rule. Enter
support(or your address's name) under Email pattern, choose Send to an email as the action, and your Tuti support address as the destination.
A rule stays off until its destination is verified. See Cloudflare's guide.
Check it
Send an email to your address from another account. Once it arrives, Receiving emails says Forwarded. On the Free plan, look for it in your Inbox.