How do I apply a down payment, which was made without an invoice, to a Project so that it appears as income in the project?

Thanks for posting to the Community, @appletreeconstru.

You can create a sales receipt when you're paid on the spot (status is automatically marked as paid) or by creating an invoice to make it appear as income in the project.

Let me show you how to apply for the down payment by using sales receipt:

1. Go to + New and then select Make a sale.
   
2. Select the project on the Customer's field.
3. Enter the amount and product/service.
4. Click Save and close.

Here's how to apply for the down payment in an invoice:

1. Go to + New and then select Send invoice.
2. Select the project on the Customer's field.
3. Enter the amount and product/service.
4. Click Save and close.

Or by going to Projects and then select the project that you've created:

1. Click Add to project on the upper right, select Invoice.
   
2. Enter the product/service and amount.
3. Click Save and Close.

You can refer to this video: How to Use QuickBooks Projects to Track Project Income & Costs.

If you want to receive deposits from customers before performing any services, you can check this article: Record a retainer or deposit.

You can always leave a message through this post if you need further assistance. I'll be arount to help. Enjoy your day!

Following @Jovychris_A advice from somewhere in the middle (you do not have an invoice and you do not have a sales receipt) choose Project and in the drop-down Receive Payment. You can receive money without an invoice or receipt and it will post to Accounts Receivable. Once you do create an Invoice you will be prompted to apply the prepayment to that invoice.

If the down payment is made in a different tax year and you are a cash basis filer you do need a sales receipt in the prior tax year although you can still use an item of prepayment income to record the cash in.  If you are accrual only the date of invoice is date of income. Example a customer pays you in full in December for a job to be completed in January. In accrual the income is in January when you create the invoice. In cash basis the payment is income when at your disposal (customer postmarks a check 12/31 but you do not get it and deposit it until 1/12, that's last year's income)