For dashboard items that are created using Raw SQL queries with variables, you can set default values for variables while embedding. While adding the embed script you can define a variables object, which should have the following structure.

/* if the id of the dashboard item is "67de24jh033889e", the variable name 
should be "draxlrVariables67de24jh033889e". Dashboard item id can be obtained 
from the Draxlr embed code
*/
<script>
	const dashboard<dashboard-id> = {
    configuration: {
      hideLastUpdated: true,
		},
    variables: {
			variableName1: value1,
		  variableName2: value2,
		}
  }
</script>
/* Draxlr Embed Script */