Counter to find the delay between a radar and an object

I am not familiar with your board. you will need to know when a pulse is sent to radar either by fpga triggering it or being informed.

On the ADC side, you receive digital signal and then you can check the values on each clock edge if it passed a given threshold. That threshold is matter of design details that you need to study and work out or experiment with your system.

Here is a chunk of code that may help

 --pseudocode
if reset = '1' then
    counter_en <= '0';
    counter <=0;
elsif rising_edge(clk) then
   if trigger = '1' then
      counter_en <= '1';
   end if;
   if adc_value > threshold then
      counter_en <= '0';
   end if;
   if counter_en = '1' then
      counter <= counter + 1;
   end if;
end if;