Numerical simulations have explored the possibility to form molecular clouds through either a quasi-static, self-gravitating mechanism or the collision of gas streams or lower-density clouds. They also quantitatively predict the distribution of matter at the transition from atomic to molecular gases. We aim to observationally test these models by studying the environment of W43, a molecular cloud complex near the tip of the Galactic long bar. Using Galaxy-wide HI and 12CO surveys we searched for gas flowing toward the W43 molecular cloud complex. We also estimated the HI and H2 mass surface densities to constrain the transition from atomic to molecular gas around and within W43. We found 3 cloud ensembles within the position-velocity diagrams of 12CO and HI gases. They are separated by 20km/s along the line of sight and extend into the 13CO velocity structure of W43. Since their velocity gradients are consistent with free-fall, they could be nearby clouds attracted by, and streaming toward, the W43 10^7Msun potential well. We show that the HI surface density, Sigma_HI=45-85Msun/pc2, does not reach any threshold level but increases when entering the 130pc-wide molecular complex previously defined. This suggests that an equilibrium between H2 formation and photodissociation has not yet been reached. The H2-to-HI ratio measured over the W43 region and its surroundings, R_H2~3.5, is high, indicating that most of the gas is already in molecular form in W43 and in structures several hundreds of parsecs downstream along the Scutum-Centaurus arm. The W43 molecular cloud complex may have formed, and in fact may still be accreting mass from the agglomeration of clouds. Already in the molecular-dominated regime, most of these clouds are streaming from the Scutum-Centaurus arm. This is in clear disagreement with quasi-static and steady-state models of molecular cloud formation.Read less <