From the fine INSERT manual:
This section covers parameters that may be used when only inserting new rows. [...]
DEFAULT VALUES
All columns will be filled with their default values, as if DEFAULT were explicitly specified for each column. (An OVERRIDING clause is not permitted in this form.)
[...]
DEFAULT
The corresponding column will be filled with its default value. An identity column will be filled with a new value generated by the associated sequence. For a generated column, specifying this is permitted but merely specifies the normal behavior of computing the column from its generation expression.
So you can use DEFAULT as a value to explicitly use the column's default value:
INSERT INTO cart(your_uuid_column) values(default);
or you can say:
INSERT INTO cart default values;
to use defaults for all the columns.