Topology optimisation seeks the best material distribution within a given domain to minimise a specific objective functional (such as structural compliance or pressure drop in fluidic systems) subject to geometric and physical constraints. Such objective functionals typically depend on the solution of full-order models (such as linear elasticity or Navier-Stokes equations), which can be computationally demanding. Moreover, the computational cost can become prohibitive when multiple queries are required for different user-defined parameters. This talk presents recent advancements in constructing surrogates for the entire topology optimisation pipeline. This is achieved by training reduced order models based on machine learning (ML) to predict educated initial guesses of the optimal layout. The proposed strategies include autoencoder-based methods, learned mapping techniques, and graph-based architectures, all integrated within a hybrid framework that combines physics-based and data-driven rationales. Numerical experiments will be presented for the optimal design of elastic structures, using various full-order topology optimisation algorithms, including homogenisation and phase-field approaches. ML-based surrogate models will be employed to predict quasi-optimal layouts for topology optimisation problems depending on user-defined parameters, in both interpolation and extrapolation settings. Finally, the enhanced performance of the resulting ML-augmented topology optimisation pipelines will be presented, highlighting the benefits of initialising the process with the ML surrogate-predicted quasi-optimal solutions.