I have not heard of or experienced problems with rodents nesting in piles of garden soil myself.
Compost and buried scraps can attract rodents, although this is something I do all the time, and rodents are not a problem, but it might be different in other places. 
Rodents will likely nest in dry, stable areas rather than a pile of loose soil. I wouldn't worry about galvanised mesh or anything like that. 
About the garden soil. Ensure you obtain high-quality garden soil, rather than poor-quality soil that may be mixed with manure and mushroom compost. Often, a premium soil doesn't need to be supplemented with fresh animal manure or have special additives to improve its quality. Adding fertiliser and compost is something you can do later once the soil is in your garden. 
I generally stay away from "homebrand" soil mixes from landscape centres because they are often inferior. If I'm going to go through the cost of buying soil I will seek out a premium professional brand. For example, I use Candy Soil 
https://candysoil.com.au/ (not affiliated), which is stocked at good garden centres around Queensland. If I'm not sure, I will ask the landscaping centre if the premium soil is from Candy. I have never had a bad load of soil from Candy, but I have had bad soil from other providers and learnt my lesson.   
Good premium soil should be black or darker grey, indicating a good mix of composted organic material. It should hold together when squeezed and then crumble when poked with your finger. The soil shouldn't be too sandy or fall through the fingers easily, nor should it be too heavy and sticky when squeezed together. It should also have small rocks or stones (inorganic material) for minerals, etc, and have an "earthy", pleasant organic smell about it, not an acidic urea smell.