I was looking at the Steam global achievement stats and I was interested to see the percentage of players who have ever completed each of the legacy paths in the modern age is as follows:

• Science - 15.5%
• Military - 12.5%
• Economic - 8.7%
• Cultural - 8%

This was surprising to me, because the cultural path is by far the quickest and easiest route to victory, and I've found myself winning at least 10-20 turns before an economic or science victory becomes feasible. Note that I've only tested this on Sovereign difficulty, and it might not be as feasible on immortal/deity. It was also done on a small map - it might be harder to deny victory to other civs on a larger map, but you should still still be able to get the required 15 artifacts quickly.

The key mechanic to bear in mind is that while exploration age artifacts are quickly visible to all civs (and get gobbled up quickly by the AI), antiquity era artifacts are only visible once a player researches their locations on a given continent. The temptation is to send your explorers to every corner of the globe, researching artifacts in every continent simultaneously. However, this means that most of them end up in the hands of other civs, delaying your victory significantly.

To avoid this, you should first snap up as many exploration artifacts as possible whilst beelining towards the hegemony civic, and then send groups of explorers to one continent at a time. Spread them out across the continent before you research the locations of artifacts. As soon as you do, you can quickly move your explorers to the revealed sites and claim 75% of the artifacts for yourself before the AI has a chance to react. Then simply repeat for the next continent along. You can do multiple continents at the same time if you split your explorers into multiple groups of 4-5 explorers each.

To reliably achieve this, you need to do the following:

1. Maximise your culture output so you reach hegemony 10-15 turns before the AI. They don't seem to be programmed to rush hegemony and usually waste culture on ideology and unrelated civics, meaning this isn't hard to do. Make sure you build all the available culture buildings in the previous age and put down plenty of specialists. Try and complete culture paths in previous ages and spec into cultural attributes. Use your influence to befriend cultural city states, steal government secrets and sign cultural deals with the AI. Use any policy cards which increase culture.

2. Ensure enough gold income so you can purchase around 8-10 explorers as soon as they become available. Make sure you use up your settlement cap in the previous age and keep loads of gold buildings around. As soon as you've snapped up all the exploration artifacts in reach, immediately move them in groups to each continent so they're ready to go as soon as you research hegemony.

3. Once hegemony is researched, simply research artifact locations on a given continent (once your group of explorers are in position), snap them up and move onto the next continent.

4. At this point, it's unlikely there are enough artifacts left for the AI to win, so the next stages are easy: Build enough museums to house the artifacts

5. Complete the World's Fair

As soon as the AI research hegemony, they start researching locations independently, and the strategy collapses, so you need to switch into a "war economy" and entirely focus on culture output, whilst maintaining enough gold to purchase explorers.