It would be the 12th day of the Omer today if you go by the molad. That would make April 11 the first day of peach. This is only to Tosphot in Sanhedrin. Most people think the present day Hebrew calendar was set up when there was real semicha but there i no record of that in the Gemara. And letters of the geonim have dates in them that do not correlate to today's calendar. To me it seems clear it was adopted during the middle of the geonic period. But with no semicha there is nothing to make it valid.