The time is last month, why don't we use Era posible and lead to other hubiera PP?
The speaker is talking in the present about an action that happened in the past, which is why we use the present perfect subjunctive.
In contrast, if the speaker were talking in the past to refer to a past action that is related to certainty in the past, then we should use the preterite, which sounds more natural. Have a look at both examples:
Es casi seguro que hayamos visto esa obra de teatro el mes pasado en Madrid.
Era casi seguro que vimos esa obra de teatro el mes pasado en Madrid.
Bear in mind that the use of a past time marker does not mean that the speaker cannot refer to that specific time in the present moment. In your example, he feels almost certain about that fact at this moment.
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