No, that is not possible with Airtable’s forms, but you have 3 good workarounds for this:
1. Give your users a link to click on which takes them to another form to add the linked record.
2. Give your users a fake linked record that is named something like “CREATE NEW RECORD”. And then, if they choose that option, reveal additional fields for them to type the new information. And then, after the form is submitted, run an automation to create the new record. Personally, I do not like this method, because it adds extra clutter & overhead to your base.
3. Use Fillout’s advanced forms for Airtable, which enables you to add new linked records from a form, and about 100 other advanced Airtable features, such as displaying as many fields as you want in a linked record picker, displaying Airtable lookup fields and rollup fields and formulas on a form, updating Airtable records from a form, and much more.