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Identify first appearance of data in an unsorted list in Google Sheets

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I have a funky lookup situation, consider this example data

Kris  |  Apr-2022  |   ?   |Kris  |  May-2023  |   ?   |Kris  |  Jun-2023  |   ?   |Pat   |  May-2023  |   ?   |Pat   |  Jun-2022  |   ?   |

In the last column, indicated by ?, I want to print the month where each person FIRST appeared in the data. So desired output given the above would be:

Kris  |  Apr-2022  |   Apr-2022   |Kris  |  May-2023  |   Apr-2022   |Kris  |  Jun-2023  |   Apr-2022   |Pat   |  May-2023  |   Jun-2022   |Pat   |  Jun-2022  |   Jun-2022   |

Now, IF the data set were ordered by date, I think I can do countifs(cell:end-of-column,cell), but the key here is that the data may be in ANY order. If that's the case, is it possible to do?

NOTE recognize that it may not be possible in one formula, happy to add helper columns with other formulas that make intermediate adjustments to the data to enable this. Will accept the answer that this is not possible to do, without sorting, I just don't have enough experience to say that. Also will not be able to do custom scripting.


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