Your form cannot create a Lead record
A HubSpot form can write to Contact, Company or Ticket. That is the complete list. The Lead object is not on it.
This surprises people who have just built a lifecycle model around the Lead object, which is exactly the point at which you go looking for it. There is no setting, no beta, and nothing you configured wrong.
What to do instead
The form populates Contact and Company. A workflow creates the Lead record downstream, when the record is worth working.
Which is the better design anyway, and it is worth being clear about why rather than treating it as a consolation prize.
Not every submission deserves a Lead record. A Lead is a working record. It represents someone a human is going to pick up. If every form fill created one, the object would fill with noise and "does an active Lead exist" would stop meaning anything, which is the exact property that makes the Lead object worth using.
The qualification logic lives in one place. A workflow can read the contact's answers, the company's firmographics, enrichment that landed after the submission, and behavior since. A form knows only what was typed into it, at the moment it was typed.
Enrichment arrives late. Company size, industry and revenue often land seconds to minutes after the contact is created. A workflow with a short delay can qualify on the enriched record. A form cannot wait for data that does not exist yet.
What goes where
Contact. The person and their intent. Name, email, phone, plus the intent fields you actually ask about: their biggest growth blocker, what they want out of this, timeline.
Company. Firmographics. Name, website, industry, plus revenue range, team size, current CRM, and whatever else you scope on. These populate through the contact-to-company association, which HubSpot links automatically by email domain.
Lead. Created downstream, by workflow, when the qualification logic says someone should work it.
Deal. Created at the opportunity moment, usually when a meeting is booked, in a pipeline chosen by a workflow reading the company and contact data you already have.
The general lesson
When a platform will not let you write directly to an object, it is worth a minute to ask whether the restriction is protecting something before you route around it.
Here it is. A Lead object that anyone can create from anywhere is a Lead object whose existence means nothing, and the whole value of the record is that its existence means something specific.