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Recently the ATLAS collaboration has reported the first results of searchesfor heavy scalar resonances decaying into a $Z$ boson and a lighter new scalarresonance, where the $Z$ boson decays leptonically and the lighter scalardecays into a top-quark pair, giving rise to $\ell^+ \ell^- t \bar{t}$ finalstates. This had previously been identified as a smoking-gun signature at theLHC for a first-order electroweak phase transition (FOEWPT) within theframework of two Higgs doublet models (2HDMs). In addition, ATLAS alsopresented new limits where the $Z$ boson decays into pairs of neutrinos and thelighter scalar resonance into bottom-quark pairs, giving rise to the $\nu \nu b\bar b$ final state. We analyze the impact of these new searches on the 2HDMparameter space, with emphasis on their capability to probe currently allowed2HDM regions featuring a strong FOEWPT. We also study the complementarity ofthese new searches with other LHC probes that could target the FOEWPT region ofthe 2HDM. Remarkably, the ATLAS search in the $\ell^+ \ell^- t \bar{t}$ finalstate shows a local $2.85\,\sigma$ excess (for masses of about 650 GeV and 450GeV for the heavy and light resonance) in the 2HDM parameter region that wouldyield a FOEWPT in the early universe, which could constitute the firstexperimental hint of baryogenesis at the electroweak scale. We analyze theimplications of this excess, and discuss the detectability prospects for theassociated gravitational wave signal from the FOEWPT. Furthermore, we projectthe sensitivity reach of the $\ell^+ \ell^- t \bar{t}$ signature for theupcoming runs of the LHC. Finally, we introduce the python package thdmTools, astate-of-art tool for the exploration of the 2HDM.

First shot of the smoking gun: probing the electroweak phase transition  in the 2HDM with novel searches for $A \to ZH$ in $\ell^+ \ell^- t \bar{t}$  and $\nu \nu b \bar{b}$ final states