You can add a running total of orders over time using a table calculation.
To create a chart similar to the one you've sketched, I would put the Order ID pill on the Rows shelf, switch it to Measure (Count Distinct), and add a table calc for Running Total. It will default to calculating a running total across the table, which is what you're looking for.
Hope this helps!
This is exactly what I am looking for. Thank you so much Dara!
Time to look up about table calculation. So much to learn in Tableau!