The building and upgrade stage can be won by anyone in the kingdom, whatever size your castle. Some may think that smaller castles have an advantage over bigger castles to rank first in this event but that is largely not the case.
Some things you can do to improve your rankings in this stage:
Save all of your resources between gathering stages and use everything you have collected on this day only.
Save all speedups you collect between upgrade stages and apply them all to building or research projects on this day only.
Speedups can be acquired through the Alliance Store and Expeditions Store and after you get the ball rolling, you will receive many speedups by simply progressing through the Building Expedition and Research Expeditions. To progress through these expeditions simply upgrade a building and apply Glory Banners to it. Alternatively, to acquire speedups through the Research expeditions complete as much research as possible in the Combat I and Combat II trees. These research trees affect your stats in the research expedition. Development, Economy, Defense, and Creation research will not help you progress through the Research Expedition.
Use speedups first on buildings that allow you to use Glory Banners and on Combat I and Combat II research. After you have run out of resources look for any additional upgrades you can do that have little or no cost (by using Splendor or Opulence Equipment and Scholar Gemstones or Savant Gemstones).
Ask your alliance leader or an R4 to use Rapid Researcher and Building Booster to receive a 20% reduction in Build and Research time.
The King of your Kingdom should use the Building Boom and Bountiful Kingdom skills to reduce building and research time an additional 20%.
Use equipment that has Research Speed and Construction Speed improvement stats, ie. Hat of Prosperity and Merchant Shoes.
Use the Development Talent which reduces build time by 20% for 5 minutes. There is a short window of time to use this but apply as many speedups as you can to your buildings during this time!
Use Guards to reduce the amount of time to research and the amount of time to construct a building. Galileo can reduce building time by 25% and research time 20% or you can use Voltaire and Dr. Van der Beek to get similar results.
Temporary Wonders can also be applied to reduce research and building times. The temporary Wonders can be purchased and used for a limited time to reduce time by 20%, switching between the Architects Compass and Book of Sciences as needed.
The total amount of speedups you use, amount of resources you have and total number of buffs to reduce build and research time will all affect your ranking in this stage. The player who applies the most upgrades and accumulates the most amount of power will ultimately take #1 in this challenge.