As @anongoodnurse pointed out, a pre-inflammatory state is present before T2D develops. Most of the patients of Type 2 Diabetes mellitus are obese. They may have dyslipidemia wherein sub-acute chronic inflammation is common.
The most common and well studied pathway is Inflammasome/IL-1β signalling. Cells have cytosolic NOD-like receptors that recognize diverse molecules that are liberated or altered. They signal via a multiprotein complex called the Inflammasome. Excess free fatty acids within macrophages and β-cells can lead to Inflammasome activation which activates an enzyme (caspase-1) which cleaves precursor form of IL-1β to it's active form. IL-1β mediates the secretion of other pro-inflammatory cytokines from macrophages, islet cells and other cells.
This is just one mechanism through which inflammation can occur. Others include accumulation of DAG, phospholipids, ceramides, etc. which are toxic lipid metabolites that can attenuate signalling through the insulin receptor and activate inflammatory pathway in the islets. Liver steatosis can also lead to inflammation and hepatocyte injury which can impair glucose homeostasis.
Robbins and Cotran Pathologic Basis of
Tsalamandris, S., Antonopoulos, A. S.,
Oikonomou, E., Papamikroulis, G. A.,
Vogiatzi, G., Papaioannou, S.,
Deftereos, S., & Tousoulis, D. (2019).
The Role of Inflammation in Diabetes:
Current Concepts and Future
Perspectives. European cardiology,
Remmerie, A., & Scott, C. L. (2018).
Macrophages and lipid metabolism.
Cellular immunology, 330, 27–42.