The HERA Collaboration, Zuhra Abdurashidova, Tyrone Adams, James E. Aguirre, Rushelle Baartman, Rennan Barkana, Lindsay M. Berkhout, Gianni Bernardi, Tashalee S. Billings, Bruno B. Bizarria, Judd D. Bowman, Daniela Breitman, Philip Bull, Jacob Burba, Ruby Byrne, Steven Carey, Rajorshi Sushovan Chandra, Kai-Feng Chen, Samir Choudhuri, Tyler Cox, David R. DeBoer, Eloy de Lera Acedo, Matt Dexter, Jiten Dhandha, Joshua S. Dillon, Scott Dynes, Nico Eksteen, John Ely, Aaron Ewall-Wice, Nicolas Fagnoni, Anastasia Fialkov, Steven R. Furlanetto, Kingsley Gale-Sides, Hugh Garsden, Adelie Gorce, Deepthi Gorthi, Ziyaad Halday, Bryna J. Hazelton, Jacqueline N. Hewitt, Jack Hickish, Tian Huang, Daniel C. Jacobs, Alec Josaitis, Nicholas S. Kern, Joshua Kerrigan, Piyanat Kittiwisit, Matthew Kolopanis, Adam Lanman, Paul La Plante, Adrian Liu, Yin-Zhe Ma, David H. E. MacMahon, Lourence Malan, Cresshim Malgas, Keith Malgas, Bradley Marero, Zachary E. Martinot, Lisa McBride, Andrei Mesinger, Jordan Mirocha, Nicel Mohamed-Hinds, Mathakane Molewa, Miguel F. Morales, Julian B. Muñoz, Steven G. Murray, Bojan Nikolic, Hans Nuwegeld, Aaron R. Parsons, Robert Pascua, Nipanjana Patra, Simon Pochinda, Yuxiang Qin, Eleanor Rath, Nima Razavi-Ghods, Daniel Riley, Kathryn Rosie, Mario G. Santos, Saurabh Singh, Dara Storer, Hilton Swarts, Jianrong Tan, Emilie Thélie, Pieter van Wyngaarden, Michael J. Wilensky, Peter K. G. Williams, Haoxuan Zheng

We report the first upper limits on the power spectrum of 21-cm fluctuations during the Epoch of Reionization and Cosmic Dawn from Phase II of the Hydrogen Epoch of Reionization Array (HERA) experiment. HERA Phase II constitutes several significant improvements in the signal chain compared to Phase I, most notably resulting in expanded frequency bandwidth, from 50-250 MHz. In these first upper limits, we investigate a small two-week subset of the available Phase II observations, with a focus on identifying new systematic characteristics of the instrument, and establishing an analysis pipeline to account for them. We report 2$σ$ upper limits in eight spectral bands, spanning $5.6 \leq z \leq 24.4$ that are consistent with thermal noise at the $2σ$ level for $k \gtrsim 0.6-0.9 h{\rm Mpc}^{-1}$ (band dependent). Our tightest limit during Cosmic Dawn ($z>12$) is $1.13\times 10^6 {\rm mK}^2$ at ($k=0.55 h{\rm Mpc}^{-1}, z=16.78$), and during the EoR ($5.5<z<12$) it is $1.78\times 10^3 {\rm mK}^2$ at ($k=0.70 h{\rm Mpc}^{-1}, z=7.05$). We find that mutual coupling has become our dominant systematic, leaking foreground power that strongly contaminates the low-$k$ modes, resulting in the loss of modes from $k=0.35-0.55$ compared to Phase I data.