Guidance on time series analysis with <10 time points

I’m working with a data set with the following structure:

list(year = c(2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008), 
    n = c(25000, 45683, 56002, 69321, 70122, 75000, 79551, 64380
    ))

As above, there are 8 total observations, and the observations (n) represent counts of people with a specific characteristic over time, measured in years. Different people are represented in different years, so this isn’t a within-subjects longitudinal design.

I am interested in measuring the effect of time on these counts, and potentially, to see whether the effect of time varies by a grouping characteristic (to be added). Because the data are in such an aggregated format, I thought that perhaps time series analysis would be appropriate, but given so few time points, I’m wondering if that’s even an option. I’m fairly new to time series analysis, so I could be off base here. Any guidance would be greatly appreciated.