I admittedly dont run very often or very well, but I just did a 5k that I only kind of prepped for, I managed to get to a consistent 7 min/km in about a week and a half of consistent attempts, granted I was walking part of that way, but when the 5k rolled around on Saturday, I did manage to do the first like 1.5 km with no walking. Obviously this isn't for everyone, but I found for me that I hate treadmills and I hate just running with no direction (even though I will wander aimlessly for hours when I'm walking) so having a set 1km lap that I could use as a baseline was really beneficial to running, and on the day of the 5k having a massive group was quite motivating to try and keep running rather than walk, regardless of how fast or slow.

I think you will for sure see results in 2 months! Keep at it :)