You should see the amount of grease that's put in new bearings used in the automotive world - the ones in A/C compressor pulleys and alternators. It's a wonder they even make it from the assembly line to the truck!
Yup ! That's why, on all sealed bearings, I always add more grease, or synthetic oil before installing the bearing.
With bearings that have rubber side shields, just lift an edge of the rubber with the point of a knife and drip a few drops of oil in. With metal shields, warm the bearing and then soak it in oil for an hour or two. The oil will get pulled into the bearing as it cools off.
Or, you can submerge the bearing in hot grease, the air trapped inside it will bubble out. When the bearing and grease cool down, any air still trapped in the bearing will also cool causing a partial vacuum, then more grease will get sucked into the bearing.
In my work with antiques sometimes there is no modern replacement bearing. It's surprising how many times old bearings can be brought back to life.
With old bearings that are not overly worn, usually the problem is just that the oil has dried out of the grease base over the years. Just add a few drops of oil and work it into the grease base by rotating the bearing. Or, do the submerge in hot oil trick.