Yes, they could. You "just" need a large mirror to concentrate sunlight on a boiler to produce the steam. Power plants that use this principle are in use today: https://en.wikipedia.org/wiki/Ivanpah_Solar_Power_Facility

The first problem you have is with economy. Burning coal is just way too cheap if you have it available, and it's much easier to get a few megawatts of heat out of burning coal than it is to get the same amount of heat from mirrors. Simply because you need about one square meter of mirror for each kilowatt of sunlight you want to collect, and the mirror needs to be continuously adjusted to the sun. A single man shoveling coal into an engine produces much, much more than just a single kilowatt of heat...

You can offset the economy problem by making coal hard-to-get in your country.

However, the second problem remains: Efficiency. Early steam engines were brutally inefficient, turning only 1% or 2% (Watt's optimized version!) of the heat into actual mechanical work. So, if you have a giant 10x10m mirror ($100m^2$), you only get 1kW or 2kW of usable power output. Anything that requires more energy than that quickly becomes infeasible to power with the many, enormous mirrors you need, which all require man-power to adjust to the sun continuously.

Of course, you can offset this by a) allowing close to modern steam turbines, and b) fancy clockworks that automagically adjust the mirrors. Nevertheless, it remains difficult to get the power from the power plants to where it's actually needed.

Yes, they could. You "just" need a large mirror to concentrate sunlight on a boiler to produce the steam. Power plants that use this principle are in use today: Ivanpah Solar Power Facility

The first problem you have is with economy. Burning coal is just way too cheap if you have it available, and it's much easier to get a few megawatts of heat out of burning coal than it is to get the same amount of heat from mirrors. Simply because you need about one square meter of mirror for each kilowatt of sunlight you want to collect, and the mirror needs to be continuously adjusted to the sun. A single man shoveling coal into an engine produces much, much more than just a single kilowatt of heat...

You can offset the economy problem by making coal hard-to-get in your country.

However, the second problem remains: Efficiency. Early steam engines were brutally inefficient, turning only 1% or 2% (Watt's optimized version!) of the heat into actual mechanical work. So, if you have a giant 10x10 m mirror ($100\ m^2$), you only get 1 kW or 2 kW of usable power output. Anything that requires more energy than that quickly becomes infeasible to power with the many, enormous mirrors you need, which all require man-power to adjust to the sun continuously.

Of course, you can offset this by a) allowing close to modern steam turbines, and b) fancy clockworks that automagically adjust the mirrors. Nevertheless, it remains difficult to get the power from the power plants to where it's actually needed.