As @stanleylawson mentioned, DA and DR are third-party matrics, so they will not increase considering your CTR or other more important things. The main criteria are getting backlinks or having an old domain.
There are some exemptions here; check this image; the website is only 44 days old, does not have that many backlinks but still has DA50. Don't know how they are doing this.
And I think, without focusing on increasing your domain authority, you should focus on providing quality to your readers, improvising your on-page game, and creating content that is worthy of ranking and getting natural backlinks.
All in all, focus more on increasing CTR, on-page UX; this might automatically help you increase your domain authority.
Focus on the following things:
Create quality content
Not Too Long, Not Too Short
Focus more on Active Voice
Use Simple Vocabulary
Keep Sentence Short and easy to Understand
Keep Paragraphs Short
Nail the TItle with High Volume Keyword
Use Keywords in SubHeadings
Optimize Your Website Structure and User Experience
Plan your site structure first
Think about information hierarchy
Prioritize URLs in your navigation bar
Categorize products by search intent
One category per blog post
Category-organized URL structure
Create a sitemap
Delete old content
Link to relevant pages
Use the pillar and cluster model
Add schema markup
Group similar keywords on one page
Optimize for people, not bots
Keep it simple
Make your Website More Mobile-Friendly
Remove bad Backlinks by Auditing your Website
As we all know DA and PA are the third party terms that is introduced by MOZ. But Google does not considered in ranking.
As per your question asked can we increase DA without backlinks then its answers is no. There are two types of authority:- DA and PA.
DA stands For Domain Authority
PA Stands For Page Authority
You will never increase your DA without making backlinks. But there is an method that works if your content is informative and unique. If someone really impress from your content that he/she will give you backlink. In this way you will increase your DA/PA.
My suggestion is to focus on producing Quality Content. Look for search intents and produce a masterpiece. What is our ultimate goal? It's to get traffic, and it does not matter what DA and PA your website has. Produce eye-catching Titles and use proper keywords for the search intents.
Yes, you can improve your website ranking without doing the off-page activity. But you have to give 100% in On-page SEO. Such as trying to write fresh and unique content for your blog. you can do keyword research for your blog on which keywords will be best for your blog. Optimize your keywords across the content. use images.
I cannot say to you that you will get an increased website DA and PA without backlinks, but if you work to build good quality backlinks to your website, then you will definitely increase your backlinks.
If you want to increase traffic on website you must follow the below steps:
Write Irresistible Headlines
Pay Attention to On-Page SEO
Target Long-Tail Keywords
Start Guest Blogging
Invite Others to Guest Blog on Your Site
Go After Referral Traffic
Post Content to LinkedIn
Implement Schema Microdata
Don’t Neglect Email Marketing
Hope this above tips will helpful on your site.
Get the fundamentals right. First and foremost, ensure that your website is properly configured.
Build a network of high-quality backlinks. High-quality backlinks are king when it comes to domain authority.
Reduce the number of low-quality backlinks. All hyperlinks are not created equal.