Auto search field without buttons, shows first result from search page

You need to search for more information on AJAX. There are some plugins that may do what you are looking for such as: https://wordpress.org/plugins/ajax-search-lite/

Alternatively, if you want to try and develop the code yourself, have a look at the following:
https://stackoverflow.com/questions/11166981/how-to-use-jquery-to-retrieve-ajax-search-results-for-wordpress
https://premium.wpmudev.org/blog/how-to-use-ajax-in-wordpress-to-load-search-results/

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