No, not right now. But that may change. As SpaceX continues to launch more satellites, the speeds which may become available have gotten higher as well.

Starlink’s top speed

Right now, Starlink’s top speed is 200Mbps. Fiber is already capable of 1000Mbps, so right now Fiber is much faster than Starlink. The planned top speed for Starlink, once all the planned satellites are in orbit, had been 1000Mbps. Now it seems that Starlink internet will be able to reach an incredible 10,000Mbps or 10Gbps. If SpaceX can achieve their goals, Starlink internet would become the fastest available internet option. Whether it is possible or not remains to be seen.

Starlink's latency

One of the draw backs of satellite internet is that it typically comes with a higher latency than ground-based competition like fiber and cable internet service providers. Fiber connections typically have a latency slightly under 20 milliseconds, which is very difficult to beat and is as close to instantaneous as it can currently get. Starlink has managed to overcome this obstacle and currently advertises latency below 20ms as well. They can do this because Starlink satellites are placed at a much lower altitude than traditional geo-stationary orbit satellites. It doesn’t stop there though, SpaceX is hoping to push Starlink internet's latency below 10ms, which would be lower than anything else to date.

If SpaceX manages to get Starlink internet’s speed up to 10Gbps and its latency to under 10ms, it will be the fastest way to access the internet that has ever existed. Of course, it still depends on whether SpaceX will be allowed to put around 30,000 satellites they plan to into orbit, and whether their calculations are accurate. Until then, it’s just speculation.