The process of matter collapsing into a black hole depends on various factors, including the distribution of matter, the amount of mass involved, and the mechanisms by which the matter can lose energy and collapse. While it's challenging to provide an exact timeframe for such an event, we can discuss some relevant considerations.
In our galaxy, the Milky Way, there are estimated to be hundreds of billions of stars, along with interstellar gas, dust, and other forms of matter. Most of the mass in the Milky Way is concentrated in the galactic center, where a supermassive black hole known as Sagittarius A* resides.
For all the matter in the galaxy to collapse into a single giant black hole, several processes would need to occur. Stars would have to exhaust their nuclear fuel and undergo gravitational collapse, leading to the formation of black holes. Gas and dust would need to lose angular momentum and fall toward the galactic center, where they could be captured by the central black hole.
The timescales for these processes can vary significantly. Stars with masses much larger than the Sun can collapse relatively quickly, within a few million years or less. Less massive stars, like our Sun, have lifetimes on the order of billions of years.
Furthermore, interactions between stars, such as collisions or gravitational interactions, could accelerate the process. However, the vast distances between stars and the low probability of such interactions make it unlikely that they would significantly speed up the overall collapse of matter in the galaxy.
Considering all these factors, it's difficult to provide an exact estimate, but it would likely take an extremely long time for all the matter in the galaxy to collapse into a single black hole. The timescale could be on the order of billions or even trillions of years, depending on the specific conditions and processes involved.