We scoped out a solution to build this using Twilio using the HubSpot API's but it was too high for the clients budget so we never implemented it. Happy to have a call and share what we had planned to do.
Yeah, there is a solution which clearly does what you mentioned - send an SMS to every new lead in Hubspot via Twilio.
Use the Hubspot Integration with Automate.io - https://www.hubspot.com/integrations/automateio
All you have to do is:
You can also get more details from here - https://automate.io/integration/hubspot-crm/twilio