@Antanas Budvytis You should have no problem doing this automatically using the API or 3rd party apps.
For example using Zapier, Make, Pipedream, etc.
Coefficient seems to have a free tier for their service here:
https://coefficient.io/connect-intercom-to-google-sheets
And here someone is explaining their process to do it without any other subscription services, keep it mind it's 2 years old some of the process may have changed.
https://medium.com/@snow.josh/how-to-connect-intercom-with-google-sheets-without-another-subscription-7ebf316a6132
With some tools you may need to do it manually for the existing leads and then setup an automation to send them as they are added in the future because many of the tools don't help with exporting the full list they only send based on a trigger action like 'New lead created'.
Hope this helps!