As soon as the Trisolarans receive Ye's transmission, the supreme leader orders their migration/invasion fleet, still under construction, to set out in the direction of the radio transmission as soon as they are able to launch. At this point in time they do not know how distant the destination is, and their vessels only have energy reserves to make a single deceleration. They have committed their entire fleet (although they do plan on building other vessels). It will be a long-term enterprise: the nearest star system will take 450 years to reach, but they don't know that that will turn out to be their destination and they must have reckoned on a much longer voyage, possibly thousands of years.
Although the Trisolarans are motivated by desperation ("God is a shameless gambler" so "we must become gamblers ourselves") there does appear to be a strategy that could mitigate some of the risk for them. Given that sophons are capable of FTL communication, and can travel at near lightspeed, they could send one or more as probes in advance of their fleet. Alternatively, if they had sent a sophon to their nearest stellar neighbour they could have discovered within 5 years that it was habitable, without the need to wait for a radio transmission.
We know that sophons are fantastically expensive to manufacture, since Project Sophon required them to cancel the building of a second fleet. However, once the equipment was in place it did not seem to take much time to successfully create 4 sophons. It's likely that the marginal cost of creating additional sophons would not have been great compared to the initial outlay.
Why didn't they adopt a strategy of exploration using sophons as probes, either as scouts in advance of their fleet, or prior to launching it?