The embeddable timeline will have that delay and there’s no way to change that, as it is not intended as a fully real-time widget.
The only limit on the streaming API is that you’ll get 1% of tweets from the firehose, and you should only use one streaming connection for your app ID. Assuming your query / filter is < 1% of the total (which is usually around 6k-7k tweets per second) then you’ll get all the tweets for your query anyway, so that’s not an issue.