Maybe.

Not much info OP. Are you planning on filtering the water? I assume it's lined, or did you use a hard shell?

Just based on your basic question I'd have to say "Yes" they will live. Most likely a short time. Depends on how great the temp fluctuates. That's stressfull on them.

My first pond was a similar size . Goldfish lived but you will need to add an oxygenator feature such as a spitter and some oxygenating plants such as hornwort and some plants to offer shade to cool the water. Water hyacinths will do nicely in a water feature this size. Big warning though... This could be the start of a ponding addiction! Shading the pond will cut algae growth. As tempting as it will be, start with only a couple of small fish. They grow and too many fish and none will survive. Remember to declorinate the water before adding fish. You can do this by letting the water stand for a couple of days or use Declor.

Most likely you will need aereation and at least some filtration to keep the water livdable and also clean so you can see the fish - Remember fish do grow so keep that in mind so goldfish should do okay.

Regardless of the pond size, aeration and filtration are essential - you did not say how big it is or size by gallonage, so maybe you treat it like a large aquarium

Here's the details.
Not sure the gallon. But the tank is 7ft long,5ft wide,2 feet deep. I have a small filter box that pumps water to my spillway.
I also have a 600gallon pump that pumps a lot of water to spillway.
There's a aretor that has 3 connections.

Don't plan to run it for the winter. So don't want to put anything in it this year but minnows.

I really don't want to run all of that 24 hours a day.
I plan to stock it with 30/40 dozen to start from local bait store.
Is that to much? To less?
The few problems I can think of are..
Will the water be to warm for them in the sun all day?
And will the water stay clean enough only running it less than half the day?

The idea behind this is that I fish a lot and rather fill my minnow bucket than wait in line at 5am. So the minnows wont stay long seeing how I will be using them a restocking weekly/monthly.

get some tall daylillys or grasses and plant where the red rocks are and that will shade the pond alot and help with the heat. and get some floating plants the minnows should be fine.

With the dimensions of the pond, that is around 500 gallons or so. If water is well aerated and shaded with plants you should be able to keep about 20 dozen minnows easily. With it in full sun, you may have to keep the equipment on alot. I have had a few minnows in my pond for several years, along with goldfish, koi and an albino catfish. Pond is in full sun and they also survived the winter. Warning: They lay alot of eggs. LOL!

Thanks for the responses.
Plan to get some water plants and make some shade.

If they lay eggs...how fast do the reproduce.
And what should I feed them?