Is it possible to send a request to the default engine?

Yes, this option is available from various connectors as well as directly from the Firebolt Python SDK.
As mentioned in SDK docs:

If the engine is not specified, your default engine is used.

If you are working directly from the API, you can instead follow these steps:

  1. Retrieve the default engine URL with this request -

curl --request GET '' \--header 'Authorization: Bearer YOUR_ACCESS_TOKEN_VALUE'
  1. Send the request to the engine by using the retrieved URL.