Should I specify my current role is part time on my resume

Have only been at my current job (auto parts sales) for a month but they made it very clear from the start that there won’t be an opportunity for me to transfer to a full time role with them.

Obviously I’m still looking for a more proper full time job. What I’m unsure about is that I feel if I put my current job on the resume, it would look like I’m “job hopping” and employers would probably be confused why I’m considering leaving after such a short time. But if I don’t it’d look like I have almost two years of employment gap. After graduating I returned to my home country to take care of my dying grandparents and some other family obligations, the arrangement made more sense financially than having my dad quit his very high paying job here in Canada (mom is estranged unfortunately). That took a bit over a year and I only landed this part time job after months of searching once I was back. The common wisdom is also that you’re more likely to be hired when you’re already employed.

What’s the best way to mitigate this issue?