There are many ways to do it.

The easiest is probably to use Zapier - https://zapier.com/apps/manychat/integrations

You can use a trigger on your Google Sheet, and the Set Custom Field action on Manychat to update the information.

You can also use Make.com https://www.make.com/en/integrations/manychat with the ‘Set a Custom Field’ action.

Or, you could add a loop in your Manychat account, to say check every hour or so if the Google Sheet has updated.

If you go down this route, be aware that you’ll have issues if you have many contacts or Google Sheets with many (thousands) of rows and data.

I was more of expecting not to use a third party application. But use Manychat to “Get Data” from Google Sheet

Option 2 will work then ;)