In a small bowl, using a fork, stir the yeast into the lukewarm water; set aside until the yeast dissolves; about 5 minutes.
In another small bowl, combine the cold water, sugar, salt, and olive oil; stir to dissolve the sugar and salt.
To make the dough using a stand mixer: fit a heavy-duty stand mixer with the dough hook attachment.
Place 5 ¼ cups flour in the mixer bowl.
Add the yeast mixture along with the cold water mixture and mix on low speed until the flour is incorporated and the dough gathers together to form a coarse ball, about 4 minutes.
Let rest 2 minutes, then mix on low speed until the dough is smooth and not sticky, about 6 minutes longer (if the dough begins to climb up the dough hook toward the motor drive, stop the mixer and push it down; if machine labors and the motor feels hot, stop and wait a few minutes for the motor to cool down).
Turn the dough out on a well-floured work surface and knead for a minute or two until it forms a smooth ball, adding up to ¼ cup flour of additional flour, if necessary.
Cut the dough in half to form even portions, each weighing 22 ounces.
With floured hands, pick up one portion of dough and pull the opposite edges together, wrapping them underneath toward the center to form a tight smooth ball; pinch to seal.
Repeat with the second portion; place each portion in a 1-gallon zip-lock plastic bag; squeeze out all the air and seal the bags, allowing enough room for the dough to double in size.
Refrigerate for at least 10 hours or up to 2 days.
Remove from refrigerator 1 hour before using to allow dough to come to room temperature; proceed with any California-style pizza.