This is difficult to answer without more understanding of what you are building, which endpoint you are using, your code, and the parameters you’ve chosen.
In my experience, Tweets posted appear very rapidly on statuses/filter and certainly much faster than on a two minute latency.
The only streaming API that is currently available commercially is enterprise PowerTrack, which is an annual contract at enterprise pricing. I’d also expect that to work more quickly than a 2 minute latency.