Obviously the best opportunity would have been to prevent Lukashenko from becoming President in 1994. Having anyone even remotely dedicated to preserving democratic institutions would have changed Belarus' trajectory.
My understanding is that he was fairly unknown as a politician when Communism fell. He was the only politician in parliament to vote against dissolving the USSRa nd becoming independent, which showed everyone then what he was like. He gained fame by being an eloquent complainer of corruption and used that to win the first Belarussian presidential election.
You need something that derails that. Perhaps an accident which kills him, or that a pro-democratic politician pre-empts his fame as a critic of corruption. The most obvious POD would be that Lukashenko's charges of corruption against Stanislav Shushkevich are found to be baseless, and Shushkevich retains his job as head of state (technically still the Chairman of the Supreme Soviet). Shushkevich then wins the first Presidential election under the new constitution in 1994.
Democratic and market reforms are instituted. Democratic parties are strengthened. There are plenty of non-democratic parties too, and it is highly likely that they will gain power at some point. At best, we can imagine a situation like Ukraine where democratic parties have extended years of control, but lost periodically to parties with less democratic credibility, but that a system of elections following democratic norms becomes accepted by the Belarussian people. Preumably, the longer the democrats retain power, the more difficult it is for someone like Lukashenko to destroy democratic institutions even if he gets power later on.
If we really want to stack the deck, we have the market reforms implemented much better in Belarus than they were in Russia or Ukraine, creating a more broad support for the democratic parties.
One thing we can say is that without Lukashenko, less emphasis will be made on continued ties with Russia, and more emphasis placed on distinctly Belarussian symbols and culture that distinguishes it from Russia.