Creating a design when you don't know the dimensions

Most billboards have an advertising agency contact number posted on them, or at the least, the company name posted who manages/owns it. Call them up with the location of the billboard and they can relay the necessary specifications for you including the type of art file required and the resolution of any bitmap images needed for producing. As posted earlier the proportions are the best first step to match if you're just doing some comprehensive renderings for ideas.

I found this site regarding standard billboard sizes

https://www.papersizes.org/billboard-sizes.htm

I also have an iphone app that is called "Measure" where I can point and click to define the 1st point on the left edge of a sign and then click a second point to define the right edge of a sign and it gives me the results in inches.

You're going to need real dimensions to get it printed anyway, so you'd only be delaying it and potentially designing to the wrong proportions. I'd say get them now.

Is this billboard frame currently empty, and not owned by an advertising company?

I would measure the billboard first.  It is important to know upfront because you will need to work in scale, typically 25% actual size.

Roy,

Your saying "a billboard" makes me (mis)interpret the question as to mean a completely new one made to fit the front.

Based on that, I should place an unfolded folding rule horizontally above the door, cross the street (after looking right and left, or left and right if you are in a place where they drive in the wrong side), take a sharp photo (preferably using a tripod), carefully cross the street again, and then File>Place (with Link clicked) the photo on the Artboard and scale the linked image to a degree that makes the folding rule have a length corresponding to the real one using a suitable (scaled) unit, preferably so you can work with the same numerical values.

Then ponder enough over the size and shape and positioning of the billboard.

Then start designing, setting the Effects>Document Raster Effects Setting high enough to have possible raster effects at a sufficient resolution at the final size (using the reverse scale for your setting it).

It may be possible to work without learning the dimensions. You can use an estimated observation, a sample signage, a sample measure. Prepare your design with highly editable features. The application should be able to make changes on your design easily when service is required. I have an application on my phone, it helps me take measurements when there is no ruler. You can take advantage of such a smart application.

You don't need the exact size, but it's important to know the proportions. For example, maybe the sign is 3 feet by 6 feet; you would know that the proportions are 1:2.

If the sign exceeds Illustrators size limits the artwork can be enlarged at the time of printing.

You could take a photo of the sign, place the photo into Illustrator and figure out the proportions from that.