You want to start a streaming job on Databricks from a particular point in time. For that you need to use the AT_TIMESTAMP position and define the JSON with the timstamp to process from:
spark.readStream.format('kinesis').option('initial_position', '
{"at_timestamp": "04-03-2026 09:38:00", "format": "dd-MM-yyyy HH:mm:ss"}')
# ...