Bring Korea into the Russian orbit definitively, and you could extend the Trans-Siberian down to Pusan. You won't get it by 1900, but that really would be an 'Orient Express'. You could even branch it into China, if there's enough Russian influence there.
The problem with any railway passing through central or southern Asia is that it would have to pass through multiple countries, often antagonistic to eachother, and multiple spheres of influence. An Orient express reaching the Pacific in OTL would need to go through the Ottoman Empire, Persia, British India, Burma, and China. You're looking at majorly unstable political situations, as well as some extremely difficult terrain.
I don't think it can be done by 1900.
Now, here's an idea: with a comprehensive Napoleonic victory, and French hegemony in Europe, you bring the German states and Austria into France's orbit. If the Ottomans and Persians can be loosely roped into the bargain (a big if), conceivably a railway could reach the Arabian Sea.
The stumbling block in such a scenario would be British India. However, assuming that the Punjab is still independent at this point, it might well welcome the development as a counterbalance to Britain's influence. This would bring the railway as far east as Lahore.
From there, though, the railway has nowhere to go. It can only turn north into Tibet, and some of the most inhospitable, mountainous, snowbound terrain in the world, or south into British India, which will hold very little attraction for the British Government as it wouldn't serve their geopolitical needs, only those of Napoleonic France (the enemy).
I very much doubt that crossing the Himalayas can be done before 1900.
And, of course, all of the above presumes the existence of masses and masses of spare money. And that nobody can think of anything better to spend it on (*cough* Suez *cough*)