Entity Resolution (ER) is the task of finding entity profiles that correspond to the same real-world entity. Progressive ER aims to efficiently resolve large datasets when limited time and/or computational resources are available. In practice, its goal is to provide the best possible partial solution by approximating the optimal comparison order of the entity profiles. So far, Progressive ER has only been examined in the context of structured (relational) data sources, as the existing methods rely on schema knowledge to save unnecessary comparisons: they restrict their search space to similar entities with the help of schema-based blocking keys (i.e., signatures that represent the entity profiles). As a result, these solutions are not applicable in Big Data integration applications, which involve large and heterogeneous datasets, such as relational and RDF databases, JSON files, Web corpus etc. To cover this gap, we propose a family of schema-agnostic Progressive ER methods, which do not require schema information, thus applying to heterogeneous data sources of any schema variety. First, we introduce two naive schema-agnostic methods, showing that straightforward solutions exhibit a poor performance that does not scale well to large volumes of data. Then, we propose four different advanced methods. Through an extensive experimental evaluation over 7 real-world, established datasets, we show that all the advanced methods outperform to a significant extent both the naïve and the state-of-the-art schema-based ones. We also investigate the relative performance of the advanced methods, providing guidelines on the method selection.