Personally, I would do this by using JotForm's advanced forms.
JotForm offers a widget called the configurable list widget, which will let you enter multiple rows on a single form.
After a form is submitted, you would then use Make's JotForm integrations and Make's Airtable integrations to bring all of the rows into Airtable as separate records.
The reason that you will need to use Make is because all of the rows will be coming in from JotForm as raw JSON, so you will need to use Make's Parse JSON module to loop through the rows.
Take a look at the 2 screenshots below to see how absolutely simple this is to setup in Make.
p.s. If your company has a budget for your project and you’d like to hire an expert Airtable consultant to help you with any of this, please feel free to contact me through my website: Airtable consulting — ScottWorld