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If you have recently build backlink, MozDa will take time to consider it. Apart from this, It also depends on not just count of backlink, it's also on your backlink quality, competitor backlink, spam score, keyword difficulty, backlink campaign, page performance and etc.
There is no such tool available in the market that can give previous ranking data. I agree with @Nozzle , Ahref and semrush can help you to get some approx idea about few keywords. Even you can use Search Console to get average position.