How to get random points from large FeatureCollection without exceeding the user memory limit?

How do you select random points from a large FeatureCollection without exceeding the user memory limit?

var bigData = ee.FeatureCollection('GLIMS/current');
var randomPoints = ee.FeatureCollection.randomPoints(bigData, 100);
print(randomPoints.size()) // Error: User memory limit exceeded

This works on smaller FeatureCollections:

var smallData = bigData.filter(ee.Filter.eq('geog_area','Iceland'))
var smallRandomPoints = ee.FeatureCollection.randomPoints(smallData, 100);
print(smallRandomPoints.size()) // 100