\begin{document}$0_1^ + $\end{document} excited state of 136Ba is performed with the full EXO-200 dataset. A deep learning-based convolutional neural network is used to discriminate signal from background events. Signal detection efficiency is increased relative to previous searches by EXO-200 by more than a factor of two. With the addition of the Phase II dataset taken with an upgraded detector, the median 90% confidence level half-life sensitivity of 2νββ decay to the \begin{document}$0_1^ + $\end{document} state of 136Ba is \begin{document}$ 2.9 \times 10^{24} $\end{document} yr using a total 136Xe exposure of 234.1 kg yr. No statistically significant evidence for 2νββ decay to the \begin{document}$0_1^ + $\end{document} state is observed, leading to a lower limit of \begin{document}$ T^{2\nu}_{1/2}(0^+ \rightarrow 0^+_1) > 1.4\times10^{24} $\end{document} yr at 90% confidence level, improved by 70% relative to the current world's best constraint."> Search for two-neutrino double-beta decay of <sup>136</sup>Xe to the <inline-formula><tex-math id="Z-20230828164210">\begin{document}${\bf 0^+_1} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/b5108f1c-5002-4976-824d-f44e832ebc23/CPC-2023-0079_Z-20230828164210.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/b5108f1c-5002-4976-824d-f44e832ebc23/CPC-2023-0079_Z-20230828164210.png"/></alternatives></inline-formula> excited state of <sup>136</sup>Ba with the complete EXO-200 dataset -
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