Does anyone know the name of the first trembling song at the beginning of Detective Conan?

You mean the song played by cello and piano before the title appeared, that is, the song before the explosion. That song is called "ピァノとチェロのためのソナタ". You should be able to find it through online search. There is also "trembling music score" in ost, but it seems incomplete after listening to it. Please search for it yourself. This should be the title of the song.

After careful investigation recently, I think it should be Beethoven's cello sonata No.3. There is a video on Youku and Tudou called "Cello Sonata No.3 by Rostovovich and richter Beethoven". You'll know after reading it. Although there is the same melody, the music in Trembling Music Score, which had a very intense rhythm before the explosion, did not completely hit a certain part of this sonata. And "ピァノとチェロのためのソナタベ?" in the soundtrack. Therefore, I think this piano and cello ensemble before the explosion is an original animation adapted according to Beethoven's cello sonata No.3 and the movie plot, and it is not completely ready-made music.