You may put estimated dates and give an explanation at the interview.
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Write the approximate dates and put an asterisk to it stating dates are an approximation due to loss of passport. Be prepared to provide some evidence towards travel in the form of airline tickets, etc.
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If you lost the passport, did you file a police report? Do you have any proof it was lost? You will have to try to reconstruct the trips and present evidence in the form of tickets or other evidence. You should always seek assistance of a good immigration attorney before filing with CIS. Yes they can check and there may be some record of your entries or departures into /out of the US. You can do Freedom of Information Act requests with various federal agencies, which I a good attorney can assist you with. Do a FOIA esp with Customs and Border Protection (CBP). Below is the link to search for AILA attorney.
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You must put your best approximation of the dates you travelled and explain that you lost the passport. If you have copies of your itineraries that should help you with the dates.
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