If you right-click on a record, you can choose “Send Record” and it will embed small thumbnails of your attachments within the email. (Note that this only works with attachments that are embedded within an “Attachment” field, not attachments that are embedded in a “Lookup” field.)
However, I don’t know of any way to automate this process of choosing “Send Record”. As far as I know, the “Send Record” functionality must be manually triggered every time.
The SendGrid email block doesn’t support embedding attachments, either — it just embeds the URL of the attachments.
So, as far as I can tell, it seems like your best bet to automate this process would be to use Integromat. Integromat can easily handle sending you an email after a form is submitted in Airtable — along with the attached attachment as well.
(My guess is that Zapier can do this as well, but in general, Integromat is more powerful, more customizable, and less expensive than Zapier.)
p.s. If you’ve never used Integromat before, it can be a little bit daunting the first time you set everything up. If you have a budget for this project and you’d like to hire an Airtable/Integromat expert to help you with this, feel free to send me a private message.