Generally speaking, you will not need to disavow any links. This should remain a last resort for toxic links. Elsewhere I describe what a toxic link is. Please understand that most junk links are not toxic. For a link to be toxic, a lot has to happen.
It is possible that there was some negative effect, however, Google understands that spam sites will make links to other sites at will and generally does not penalize the target site (yours). In fact, enough spam links can help some by adding up tiny bits of value. I know of one site that has 58,000 spam links from two related sites and performs rather well because of them despite the very few links of value it has obtained. I am not suggesting that spam links are good- just not necessarily bad.
In your case, the site is new and any knock will really hurt. All new sites fluctuate wildly for a period while Google fills it's index and creates the various scores required. This can take months to do and any recalculation and refresh will effect your placement in the SERPs from day to day and even hour to hour. This is also of course dependent upon he search and competition for the search terms.
Do good work in creating your site and doing decent and honest SEO and your site will perform just fine in the end.
BTW- the various SEO websites are very incomplete and slow to keep up with changes. Do not count on them. The experts are Google's various tools. I suggest sticking to just these at least for a while.