First, make the guava cake. Position a rack in the center of the oven and preheat the oven to 350°F. Generously spray an 9 x 13-inch pan with cooking spray and line the bottom with parchment paper. Spray the parchment, too.
Mix the dry ingredients. In a medium bowl, whisk together the flour, baking powder, and salt.
Mix the wet ingredients. In a large liquid measuring cup, whisk together the guava, milk, vanilla, and food coloring.
Cream the butter, sugar, and oil, then add the egg whites. In the bowl of a stand mixer fitted with the paddle attachment, combine the butter, sugar, and oil. Beat on medium until light, fluffy, and doubled in volume, 3 to 4 minutes, using a rubber spatula to scrape down the bottom and sides of the bowl as necessary. Reduce the mixer to low and add the egg whites in 3 additions, adding the next addition only after the previous one has been fully incorporated and scraping down the bottom and sides of the bowl after each addition. Alternate adding the dry and wet ingredients. With the mixer still on low, add the the dry ingredients in three parts, alternating with the wet ingredients in two parts, beginning and ending with the dry ingredients. Beat until just combined, then scrape down the bottom and sides of the bowl once more, then beat on low for an additional 30 seconds.
Assemble the cake for baking. Pour the batter into the prepared pan and use an offset spatula to smooth its top if necessary.
Bake the cake. Bake for 25 to 30 minutes. When done, the top of the cake should bounce back when gently pressed and a skewer inserted into the center of the cake should come out with a few crumbs attached. Cool completely in the pans on a wire rack before frosting. Once the cake is cool, make the guava cream cheese frosting. In the bowl of a stand mixer fitted with the whisk attachment, whisk the cream on medium-high speed until stiff peaks form, 4 to 5 minutes.Transfer the whipped cream to a medium bowl. Beat the cream cheese, sugar, food coloring, and salt for the frosting, then add the guava puree. Replace the whisk attachment with the paddle attachment. Combine the cream cheese, sugar, food coloring and salt in the stand mixer bowl (there's no need to clean the bowl!). Beat on medium-low until soft and creamy, 2 to 3 minutes.Reduce the mixer to low and add the guava puree in 4 additions, adding the next addition only after the previous one has been fully incorporated and scraping down the bottom and sides of the bowl after each addition. Once incorporated, scrape down the bottom and sides of the bowl once more, then beat on medium-high until the frosting is creamy and smooth, 2 to 3 minutes. Fold the whipped cream into the frosting. Scoop half of the whipped cream over the frosting and fold it in with a rubber spatula. Repeat with the remaining whipped cream and fold them in until just combined. At this point, it will be a very light and fluffy frosting.
Assemble the guava sheet cake. Use an offset spatula to cover the top of the cake with the frosting completely. Garnish with sprinkles. Serve and store. Serve immediately at room temperature. If serving and storing for later, refrigerate for at least 2 hours to keep the frosting cool and fluffy. Thaw at room temperature for 30 minutes before serving.The cake will keep, loosely covered in plastic wrap, in the refrigerator for up to 3 days.