Imagine you cut you finger, allowing some virus to enter your body. This infects some of your cells, forcing them to make more virus.

The damaged tissue leads to release of inflammation markers like interleukins, alerting your innate immune system to the situation. They hightail it to the site of the cut and pick up the fight. In essence, they try to kill all virus infected cells to stop the virus replication. Some cells can even signal to immune cells that they have been hijacked by a virus. The innate immune response is not enough to get you healthy again if it is a serious infection, but is a first effort and it buys you time. During this „battle“ a lot of debris is made. Remains of killed cells, components of the virus etc. Antigen-presenting cells (APCs) grab a piece of the rubble and the move to the next lymph node. A chemokine trail shows them where to go. Once there, they take this piece of debris and put it into a special protein on their surface called MHC. This allows them to present this antigen (piece of debris) to other cells.

In the lymph node, there are a lot of naive B and T-cells. Each of these has a different B or T-cell receptor. How it is shaped and what antigen it recognises is randomised at its “birth” through a process called VDJ recombination.

The antigen presenting cells now shows it’s piece of debris around to many naive T or B cell until one happens to bind it with its receptor. This cell is then rapidly copied millions of times. Once this army of T-cells is released into the blood, it can very specifically fight off any virus infected cells. B cells make antibodies and release that instead. That way, your immune system can fight even previously unknown invaders.

Your initial assumption can still be true - maybe the right T-cell lives in your leg at the moment you are cut. But the lymphatic system is all connected. APCs and other cells move through it as needed. This turns the node nearest to the site of infection into a sort of forward operating base that is still connected to the other nodes.

You also do not need a perfect match. If you found a T-cell or B-cell that can bind the antigen, the part it uses to recognise the virus can be optimised in a process called avidity maturation. You can also have many matches, with a number of different naive B cells or T cells being activated and then copied. This is the normal case. If you get infected, the antibodies in your blood are polyclonal, meaning they come from many different initial naive B-cells. Two different B-cells lines can make antibodies recognising the same or different parts of a virus. This redundancy is beneficial, it lowers the chance that a mutation of the virus allows it to escape the immune response, because the initially recognised antigen is no longer present. The process also continuously optimises the capability to recognise and fight the virus. Redundancy, with many parts trying to do the same task is key to not dying if the virus outsmarts any one system.