How to solve this depends very much how you store it.
In general I would be aware of letting WordPress handle historical dates, of broad range, as post dates. There are various limitations that you can check on this site or eg. trac.
Date query for yesterday
If you create a datetime object with:
$dto = DateTime::createFromFormat( 'Y-n-j', current_time( 'Y-n-j' ) );
where the timezone is included in the current_time(), then you can try to set it to the day before with:
$dto->modify( 'yesterday' );
The month and day for yesterday should be accessible with:
'date_query' => [
[
'month' => $dto->format('n'),
'day' => $dto->format('j'),
],
],
For 2 days before we can try
$dto->modify( '-2 days' );
and so on
Date query for the current date or the previous available date
If you use the same year for all events, then you can use:
'date_query' => [
[
'before' => current_time( 'Y-n-j' ),
'inclusive' => true,
],
],
Alternatives
For a very sparse month-day list, one could try to group posts by month and day to find the previous available post date. But this would need a custom query.
One could also use a custom database table to store the dates, for more flexibility, but that also needs a custom building.
Many event plugins store the dates in the post meta, and use meta_query in WP_Query to filter through it. But this might not scale well for large number of posts.
We could even use a custom taxonomy to store the month-day, but then the month-day ordering might get tricky.