Answer: The Gemara (Megilla 32a) writes that there is a machlokes as to whether one who is called up to the Torah should leave the sefer Torah open or close it while they are reciting the berachos before their aliya. According to R’ Meir, one should close the sefer Torah so as not to give off the impression that the berachos are in the Torah. R’ Yehuda, however, is not concerned that people will make this mistake. The Gemara says that the halacha follows R’ Yehuda. Thus, Rambam (Tefilla 12:5) and the Shulchan Aruch (OC 139:4) write that when called up, one should open the sefer Torah to see where they are going to read from, leave the Torah open while saying the berachos and then read. One should roll the sefer Torah closed before saying the berachos after their aliya.
The Taz (OC 139:4) and Mishna Berura (139:17) explain that one shouldn’t close the sefer Torah as rolling it back and forth and finding the place again would constitute tircha detzibbura, an unnecessary burden on the community.
The Rema (OC 139:4) adds that when saying the berachos beforehand, one should look to the side. Nonetheless, the Mishna Berura (139:19) writes that this isn’t ideal as it looks like one is looking away. Rather, one should close one’s eyes, or read the berachos if they are on the bimah.
Some follow Tosafos (Megilla 32a) who writes that ideally one should close the sefer Torah before saying the berachos. The Aruch Hashulchan (OC 139:12) challenges this, however, saying that the consensus of poskim is to leave the sefer Torah open.
In conclusion, it is preferable to leave the sefer Torah open during the first berachos so as not to delay the tzibbur by even a few extra seconds.