With regard to finding the filing date used to determine the statute of limitations period, the Account Transcript or Record of Account transcript of the taxpayer will show this date on the line labeled "RETURN DUE DATE OR RETURN RECEIVED DATE (WHICHEVER IS LATER)." (Presumably the line is labeled this way to avoid taxpayers questioning an April 15 date being shown when they actually submitted their tax return earlier.) The transcript also has an entry labeled "Tax return filed," but the date on that line just represents the date that the entry was made to the transcript, not the filed date, and can be considerably later than the filed date.
Another complicating factor is that the IRS allows an unadvertised grace period with respect to the regular due date of tax returns, so it's possible that a tax return filed shortly after the regular due date will be marked as having been filed on the regular due date. For example, I filed my 2018 tax return under extension on April 20 yet my Account Transcript shows a filing date of April 15.
