To add an estimate to a project, make sure to select the name of the project in the Customer field. With that said, you can edit the estimate you sent so that it shows on the Project page. I'd be happy to show you how:
On the left pane, select Sales.
Go to the All Sales tab.
Click the Filter tab and select Estimates under Type.
Select the estimate on the list.
From the Customer drop-down list, select the name of the project.
Click Save and close.
Once done, you can go back to the Projects page to create an invoice from the estimate. I've attached some articles you can use as a reference on how to split estimates to multiple invoices and track profitability: