As Peter mentioned, you can use Lucene syntax out-of-the-box to search using a "starts with" functionality. This works best if you are performing a field-specific search or if your visitors know to add the "*" to the search.
You could also change the analyzer to "Starts with": https://docs.kentico.com/k11/configuring-kentico/setting-up-search-on-your-website/using-locally-stored-search-indexes/configuring-search-assistance-features-for-local-indexes#Configuringsearchassistancefeaturesforlocalindexes-Substringsearch. This will tokenize all fields marked Tokenize into substrings allowing for a "starts with" functionality for all fields without the use of the "*" character.