Probably not.
At any rate you would want to bring into the garage the cooler evening air so skip solar.

Measure the temp in the area and see what happens. I get about 10 degrees hotter in the attic and garage during the day without a fan.

My two cents worth-for free
 

Cooling effect
Depends on how you feel as opposed to thermometer reading.
Reason is simple. Your body cools based on sweat-water evaporation. Moving air evaporates more sweat so you feel cooler.

Sticking a fan in your garage running on automatic
I would not do it. You/I have all kinds of flammable stuff in the garage. Car, paint, sawdust, to mention a few. A fan introduces more oxygen-remember fanning charcoal, a campfire etc. Properly installed there should be a thermal disconnect.
Simple and cheap. I have a fan that I only run when I am working on something in the garage.

Solar fan
Since as described above my use in minimal I would not see any cost savings. For me a viable system would require the collector plus a battery to store the electricity. So the cost goes up as well as the space required.

A fan and air flow
Think of sucking air out of a coke bottle. Nothing will happen,
You need to allow air to get into the bottle as well as trying to such it out. So you need to install intake vents of some kind.
A fan will be rated at free air flow. Vents are not 100% efficient
so the rated flow is reduced in the real world.

This is something I never considered. The solar fan will run during the cooler weather because there's no way to stop it.

Garage Door Insullation
 

We have a West facing garage. I installed garage door insulation which I believe I purchased at Lowe's but possibly HD. only took a couple hours to install on an oversized door plus a golf cart door and it made a SIGNIFICANT difference in temperature in the garage. I also keep the attic stairs and the window cracked open which creates a natural airflow helping to keep the temperature down at zero recurring expense.

Kindly suggest to be careful leaving an unprotected opening in the garage ceiling, if there is a fire, that provides a direct path for flames into the attic.

Same for ventilation fans, they should have a fire damper that automatically closes in the presence of flames. An example:

Access Denied

What do you mean by a significant difference in temperature? I have a West facing garage, with no vents, no insulation, no fans, and no shade. The temperature in the garage almost never exceeds about 6 degrees above the outside air temperature. In the morning my garage temperature is less than the outside air temperature. Garage door insulation alone can only slow down the heat transfer, but it cannot change the eventual equilibrium temperature.

I have a horizontal screen sliders on my garage door and since our laundry is in the garage, we found it best to keep the garage door open and the screens closed is cooler than the garage door closed. For a few years I cracked the attic steps opening about 6" and I could feel a steady breeze in the garage by the opening and the garage felt better overall.

However, I have since kept the attic steps opening shut for the last couple of years for two reasons. Termites will usually die quickly in temperatures above 100 degrees, I don't want to give them a place to breed. In a masonry home the wooden trusses are my biggest concern and leaving the attic access open creates a greater chance of any fire in the garage spreading quickly.