How can one get traffic on a blog without any SEO tool?
Hi! According to your question, you do not want to use a paid SEO tool. Paid tools often work well but for a limited period. Initially, I struggled to get web traffic. But now the results are in my favor. I will proceed to answer based on my experience.

It is a fact that tools usually have limited set of capabilities. They may become ineffective soon. As a solution to this, I opted for the following free methods in my case:
1) Social Media Posts
This lets you show off your content to more people and build an audience. These social media posts should show off what’s interesting about your content and engage viewers. You need to do some research on that.
2) Backlinking
Hyperlinks or web links connect one page or post with another page or post. While writing blogs, do not forget to mention the link to your main website. However, where and when to use backlinking depends on your situation.
You can try those for free and leave me a reply about your experience.
I have also tried One Minute Traffic Machines. The best thing I like about it is, OMTM teaches a different free traffic-getting method. For me, the results are fantastic as I apply their techniques for all my websites. I hope you will get your desired results too.
Above all, your focus and consistent effort will determine whether you succeed.
Good Luck!
Cleo