Is there a option to ad COGS starting from a specific date?

There is an option to do that! The setting is called the "Database COGS Sync Setting" which can be enabled on this page here. A full explanation of the setting is here: How does the "Database COGS Sync" work?

With this setting enabled, you can update the COGS value for this product in Profit Calc and it will only apply to new orders going forward.

If there are previously synced orders from today that need to be updated let me know in the bottom right and I could do a custom COGS sync on the backend here just for those orders.