Solo founder here. Make a product that people want and are willing to pay for. The product may be in what appears to be a crowded field. Identify niche opportunities or cases where an established leader is doing a poor job. It's fine to do some consulting on the side to pay the bills. Of course it will take time away from the product you are building; just be able to recognize when it's too much and scale back consul…
I’m a full time software engineer for a small company. No amount of googling answers my question: what exactly is part time consulting? At least, in your context
The full-time employment entity is your own company (if you are the founder) or your full-time employer and there could be other companies or individuals to whom you work for part-time (1 day a week, adhoc days/hours, weekends etc) and you are paid for that work.
You have two things to consider:
1. Make sure it is legal (for example if you are on certain types of work-permit visa in some countries it might be illegal to work for anyone other than the work visa sponsor).
2. Make sure you don't have conflict in your employment contract clauses (many full-time employment contracts have clauses that prevent you from working for others even for part-time without explicit permission from the full-time employer).
Usually if you ask your full-time employer, they may permit you to do one-off consultations to other companies (and get paid for it) if they think it would not take your focus away from your FTE work and if there is no conflict of interest or potential to reveal trade-secrets (example: if that other company is a competitor etc).